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Prabhu, Nagabhushana 1966. "Aspects of solition physics : existence of static solitons in an expanding universe and quantum soliton-antisoliton annihilation". Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47461.
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Zamaklar, Marija. "Solitons on branes and brane solitons in supergravity theories". Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620358.
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Bahri, Yakine. "Stability of solitons and multi-solitons for Landau-Lifschitz equation". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX028/document.
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Dans cette thèse, nous étudions l'équation de Landau-Lifshitz avec une anisotropie planaire en dimension un. Cette équation décrit la dynamique de l'aimantation dans des matériaux ferromagnétiques. Elle admet des solutions particulières de type onde progressive appelées solitons.D'abord, nous montrons la stabilité asymptotique des solitons de vitesse non nulle appelés solitons sombres dans l'espace d'énergie. Plus précisément, nous prouvons que toute solution correspondant à une donnée initiale proche du soliton de vitesse non nulle, converge faiblement dans l'espace d'énergie en temps long, vers un soliton de vitesse non nulle, sous les invariances géométriques de l'équation. Notre analyse repose sur les idées développées par Martel et Merle pour les équations de Korteweg-de Vries généralisées. Nous utilisons la transformée de Madelung pour étudier le problème dans le cadre hydrodynamique. Nous invoquons ensuite la stabilité orbitale des solitons et la continuité faible du flot afin de construire le profil limite. Nous établissons de plus une formule de monotonie pour le moment, ce qui nous permet d'avoir la localisation du profil limite. Sa régularité et sa décroissance exponentielle découlent d'un résultat de régularité pour les solutions localisées des équations de Schrödinger. Nous finissons la preuve par un théorème de type Liouville, qui nous indique que seuls les solitons vérifient ces propriétés dans leurs voisinages.Nous nous intéressons également à la stabilité asymptotique d'une superposition de plusieurs solitons appelées multi-solitons. Les solitons de vitesse non nulle sont ordonnés selon leurs vitesses et sont initialement bien séparés. Nous démontrons la stabilité asymptotique autour et entre les solitons. Plus précisément, nous montrons que pour une donnée initiale proche de la somme de $N$ solitons sombres, la solution correspondante converge faiblement vers un des solitons de la somme, quand elle est translatée au niveau du centre de ce soliton, et converge faiblement vers zéro quand elle est translatée entre les solitonsIn this thesis, we study the one-dimensional Landau-Lifshitz equation with an easy-plane aniso-tropy. This equation describes the dynamics of the magnetization in a ferromagnetic material. It owns travelling-wave solutions called solitons.We begin by proving the asymptotic stability in the energy space of non-zero speed solitons More precisely, we show that any solution corresponding to an initial datum close to a soliton with non-zero speed, is weakly convergent in the energy space as time goes to infinity, to a soliton with a possible different non-zero speed, up to the geometric invariances of the equation. Our analysis relies on the ideas developed by Martel and Merle for the generalized Korteweg-de Vries equations. We use the Madelung transform to study the problem in the hydrodynamical framework. In this framework, we rely on the orbital stability of the solitons and the weak continuity of the flow in order to construct a limit profile. We next derive a monotonicity formula for the momentum, which gives the localization of the limit profile. Its smoothness and exponential decay then follow from a smoothing result for the localized solutions of the Schrödinger equations. Finally, we prove a Liouville type theorem, which shows that only the solitons enjoy these properties in their neighbourhoods.We also establish the asymptotic stability of multi-solitons. The solitons have non-zero speed, are ordered according to their speeds and have sufficiently separated initial positions. We provide the asymptotic stability around solitons and between solitons. More precisely, we show that for an initial datum close to a sum of $N$ dark solitons, the corresponding solution converges weakly to one of the solitons in the sum, when it is translated to the centre of this soliton, and converges weakly to zero when it is translated between solitons
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Harland, Derek. "Chains of solitons". Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2303/.
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We construct and analyse chains of solitons in various field theories. Particular emphasis is placed on the constituent structure, which appears to be be a generic feature of chains. In Yang-Mills theory, we construct axially symmetric chains of instantons (calorons) with instanton charge 2, making essential use of the Nahm transform. We show that there are two distinct families of caloron, which can be distinguished using representation theory. We also construct calorons on hyperbolic space with instanton charge 1 and monopole charge 0. This generalises earlier work of Garland and Murray, in the same way that non-integer-mass hyperbolic monopoles generalise the integer-mass hyperbolic monopoles of Atiyah. We study chains of skyrmions with charge 1 in both the Skyrme and planar Skyrme models, using various approximate analytic Ansätze. In the Skyrme model chains are argued to exist and to have an energy per baryon number lower than the charge 2 skyrmion. In the planar Skyrme model, we show that the stability of chains depends on the choice of potential function. We study chains and kinks in the CP(^n) sigma models analytically, in particular, we show that chains are kinks in a sigma model whose target is a homogeneous space for a loop group. This is the Sigma model analog of the statement that a caloron is a monopole whose gauge group is a loop group.
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Suntsov, Sergiy. "DISCRETE SURFACE SOLITONS". Doctoral diss., University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2901.
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Surface waves exist along the interfaces between two different media and are known to display properties that have no analogue in continuous systems. In years past, they have been the subject of many studies in a diverse collection of scientific disciplines. In optics, one of the mechanisms through which optical surface waves can exist is material nonlinearity. Until recently, most of the activity in this area was focused on interfaces between continuous media but no successful experiments have been reported. However, the growing interest that nonlinear discrete optics has attracted in the last two decades has raised the question of whether nonlinear surface waves can exist in discrete optical systems. In this work, a detailed experimental study of linear and nonlinear optical wave propagation at the interface between a discrete one-dimensional Kerr-nonlinear system and a continuous medium (slab waveguide) as well as at the interface between two dissimilar waveguide lattices is presented. The major part of this dissertation is devoted to the first experimental observation of discrete surface solitons in AlGaAs Kerr-nonlinear arrays of weakly coupled waveguides. These nonlinear surface waves are found to localize in the channels at and near the boundary of the waveguide array. The key unique property of discrete surface solitons, namely the existence of a power threshold, is investigated in detail. The second part of this work deals with the linear light propagation properties at the interface between two dissimilar waveguide arrays (so-called waveguide array hetero-junction). The possibility of three different types of linear interface modes is theoretically predicted and the existence of one of them, namely the staggered/staggered mode, is confirmed experimentally. The last part of the dissertation is dedicated to the investigation of the nonlinear properties of AlGaAs waveguide array hetero-junctions. The predicted three different types of discrete hybrid surface solitons are analyzed theoretically. The experimental results on observation of in-phase/in-phase hybrid surface solitons localized at channels on either side of the interface are presented and different nature of their formation is discussed.Ph.D.
Optics and Photonics
Optics and Photonics
Optics PhD
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Morandotti, Roberto. "Discrete optical solitons". Thesis, University of Glasgow, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300979.
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Zárate, Devia Yair Daniel. "Phase shielding solitons". Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/115388.
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Magíster en Ciencias, Mención FísicaLos solitones son el fen omeno universal m as profundamente estudiado, debido a los innumerables sistemas físicos en los cuales se observa. Estas soluciones corresponden a estados localizados y coherentes que surgen naturalmente en sistemas extendidos, siendo una de sus propiedades m as fascinantes el hecho de que pueden ser tratados como partículas macroscópicas a pesar de estar formados por numerosos componentes microscópicos. Desde su primera descripci on, realizada por J. S. Russell en 1884, el estudio de solitones se centró en sistemas conservativos por más de cien años. Sin embargo, los pioneros trabajos de Alan Turing e Ilya Prigogine demostraron que los sistemas fuera del equilibrio se auto{ organizan por medio de la generación de estructuras disipativas. Hoy en día, sabemos que es justamente este mecanismo el que permite la formación de solitones disipativos en sistemas con inyección y disipación de energía. Nuestro principal interés ha sido caracterizar de forma analítica y numérica a los solitones que emergen en sistemas forzados paramétricamente{sistemas forzados por medio de un parámetro efectivo que var a en el espacio y/o tiempo. Los sistemas forzados param etricamente pueden experimentar una resonancia paramétrica, la cual se caracteriza por una respuesta subarm onica (subm ultiplos de la frecuencia natural del sistema). Dada la complejidad que presentan los sistemas paramétricos, focalizamos nuestro estudio en la ecuación de Schrödinger no lineal disipativa forzada paramétricamente (PDNLS). Este modelo caracteriza bien la din amica de sistemas forzados param etricamente, en torno al punto de aparición de la resonancia paramétrica, en el límite de baja disipación e inyección de energía. Los solitones disipativos, presentes en PDNLS, típicamente muestran una estructura de fase uniforme. Dichas estructuras han sido ampliamente utilizadas para describir a los solitones hidrodinámicos que aparecen en el experimento de Faraday, estados localizados de la magnetización en un hilo magnético, o los clásicos solitones presentes en una cadena de péndulos con soporte verticalmente vibrado, entre otros. Por medio de simulaciones numéricas interactivas de solitones disipativos en la ecuaciónPDNLS, hemos logrado observar una interesante din amica de frentes de fase hasta ahora desconocida. Estos frentes de fase se propagan hasta alcanzar un punto de equilibrio estacionarioarbitrario. A este tipo de solitones los hemos llamado solitones escudados por la fase (phase shielding solitons), dado que la estructura nal de fase pareciera proteger al módulodel solit on. Hemos logrado caracterizar anal ticamente estas soluciones localizadas, determinando ocho posibles con guraciones. Los solitones estudiados poseen una talla característica dada por el tamaño de la estructura de fase estacionaria. Adem ás, extendimos nuestro estudio al caso bidimensional, mostrando los resultados, dos tipos de phase shilding solitons bidimensionales; axialmente simétricos y asimétricos. Los primeros pueden ser entendidos como una rotación en 2 de las soluciones simétricas encontradas en el caso unidimensional. Por su parte, las soluciones asimétricas bidimensionales presentan propiedades mucho más interesantes, ya que su estructura nal de fáse contiene todas las con guraciones halladas en el caso unidimensional. Con el n de corroborar la existencia de solitones disipativos con estructura de fase no uniforme en sistemas físicos, realizamos simulaciones numéricas de diversos sistemas paramétricos reales. Satisfactoriamente, concluimos que el fenómeno phase shielding soliton es universal, y esperamos que pueda ser prontamente observado experimentalmente.
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Hivet, Romain. "Solitons, demi-solitons et réseaux de vortex dans un fluide de polaritons". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00911207.
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Ce travail est consacré à l'étude des fluides quantiques de polaritons de microcavités semi-conductrices et en particulier à la génération de solitons, de demi-solitons et de réseaux de vortex. Nous avons développé un dispositif expérimental permettant la génération et l'observation de solitons sombres dans un fluide de polaritons. Nous observons les profils de densité et de phase caractéristiques des solitons, et étudions leurs propriétés de stabilité. Nous montrons expérimentalement que l'utilisation d'une pompe polarisée linéairement mène à la formation de demi-solitons, grâce au champ magnétique effectif existant en présence des deux populations de spin. Après avoir caractérisé les demi-solitons en densité et en phase, une tomographie complète du système est effectuée pour extraire l'information stockée dans le pseudospin. Ces études nous permettent de formuler une analogie formelle entre les demi-solitons et les monopoles magnétiques. Enfin, nous nous intéressons à des techniques de piégeage de vortex. Nous mettons à profit l'utilisation de masques métalliques pour créer des puits de potentiels piégeant les vortex générés hydrodynamiquement lors de l'écoulement du fluide sur un défaut à basse densité de polaritons. Nous utilisons ces masques pour réaliser des réseaux géométriques de vortex et d'antivortex à basse densité de polaritons dont la forme et la taille sont contrôlables. L'étude des effets d'interaction polariton-polariton à haute densité menée grâce à un dispositif expérimental à plusieurs faisceaux d'excitations nous permet d'observer la déformation et la destruction du réseau dues à l'annihilation des paires vortex-antivortex.
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Irwin, P. "Classical and quantized solitons". Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604958.
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This thesis is concerned with the classical and semi-classical behaviour of solitons in three dimensions. In Chapter 2 we consider the zero mode quantization of the minimal energy Skyrmions for nucleon numbers between four and nine and also the conjectured solution with nucleon number of seventeen. The method relies on determining the contractibility of the loops in the configuration space corresponding to the discrete symmetry of the minimal energy solution. We find that for nucleon numbers four, six and eight the ground states obtained agree with the observed quantum numbers of the ground states of Helium, Lithium and Beryllium. But for nucleon numbers five, seven, nine and seventeen the spins obtained conflict with the observed isodoublet nuclear states. In Chapter 3 we discuss the gradient flow curves for two well-separated Skyrmions. The form of the equations are quite simple and lead to an unambiguous interpretation of how the solution curves behave. There exists a large number of symmetries which enable us to find the solutions in closed form in the case of massless pions. An algorithm is described that estimates the positions and relative orientation of two-separated Skyrmions, given the numerically generated Skyrme field. Chapters 4 and 5 are concerned with monopoles in SU(3) gauge theory. In Chapter 4 we consider charge two monopoles in the minimally broken case. A certain class of solutions looks like SU(2) monopoles embedded in SU(3) with a transition region or "cloud" surrounding the monopoles. We solve for the long-range fields in this region, confirming the existence of the cloud. The moduli space metric found by Dancer, is expressed in an explicit form. Chapter 5 discusses the case of maximal symmetry breaking for SU(3) monopoles for magnetic charge (2,1). Some properties of this space are discussed, we also find the axially symmetric geodesic submanifold of the moduli space and study the case of monopole scattering there. We analyse the limit where minimal symmetry breaking occurs, comparing to the results in Chapter 4.
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Shiiki, Noriko. "Solitons and black holes". Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313504.
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Ruback, Peter Julian. "Solitons and moduli spaces". Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238701.
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Wong, Kenny. "Applications of topological solitons". Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708436.
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Russell, Katherine. "Field theory and solitons". Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2205.
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Batista, Rondinelle Marcolino. "Rigidez de solitons gradiente". Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoNosso objetivo nesse trabalho à apresentar um teorema que caracteriza os solitons gradiente rÃgidos para caso nÃo compacto. Como aplicaÃÃo provaremos que os solitons gradiente homogÃneos sÃo rÃgidos e apresentaremos um exemplar de soliton de Ricci que nÃo pode ser gradiente.
Our goal in this work is to present a theorem which characterizes the gradient solitons rigid for non-compact case. As an application we prove that the homogeneous gradient solitons are rigid and provide an example of the Ricci soliton can not be gradient.
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Betancourt, de la Parra Alejandro. "Cohomogeneity one Ricci solitons". Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:8f924daf-d6e6-4150-96c2-d156a6a7815a.
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In this work we study the cohomogeneity one Ricci soliton equation viewed as a dynamical system. We are particularly interested in the relation between integrability of the associated system and the existence of explicit, closed form solutions of the soliton equation. The contents are organized as follows. The first chapter is an introduction to Ricci ow and Ricci solitons and their basic properties. We reformulate the rotationally symmetric Ricci soliton equation on Rn+1 as a system of ODE's following the treatment in [14]. In Chapter 2 we carry out a Painlevé analysis of the previous system. For the steady case, dimensions where n is a perfect square are singled out. The cases n = 4, 9 are particularly distinguished. In the expanding case, only dimension n = 1 is singled out. In Chapter 3 we reformulate the cohomogeneity one Ricci soliton equation as a Hamiltonian system with constraint. We obtain a conserved quantity for this system and produce explicit formulas for solitons of dimension 5. In Chapter 4 we introduce the notion of superpotential and use it to produce more explicit formulas for solitons of steady, expanding and shrinking type. In Chapter 5 we carry out a Painlevé anaylsis of the Hamiltonian corresponding to solitons over warped products of Einstein manifolds with positive scalar curvature. This analysis singles out the cases discussed in the previous chapters. We also carry out an analysis of the Hamiltonian corresponding to the Bérard Bergery ansatz [5]. This analysis singles out a 1-parameter family of solutions.
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Woodford, S. R. "Parametrically driven dark solitons". Master's thesis, University of Cape Town, 2004. http://hdl.handle.net/11427/4946.
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Includes bibliographical references (leaves 120-127).This is a study of the dynamics of the dark solitons described by the parametrically driven nonlinear Schrödinger equation. We prove that both types of dark solitons (the Bloch and Néel walls) are stable throughout their existence regions, and that in the region of their coexistence, a family of Bloch-Néel bound states exists, which is parametrised by the inter-soliton separation. Using the Hirota method, we explicitly construct the family.
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Batista, Rondinelle Marcolino. "Rigidez de solitons gradiente". reponame:Repositório Institucional da UFC, 2013. http://www.repositorio.ufc.br/handle/riufc/7218.
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BATISTA, Rondinelle Marcolino. Rigidez de solitons gradiente. 2013. 70 f. Dissertação(Mestrado em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Programa de Pós-Graduação em Matemática, Fortaleza, 2013.Submitted by Erivan Almeida (eneiro@bol.com.br) on 2014-02-06T15:52:29Z No. of bitstreams: 1 2013_dis_rmbatista.pdf: 475768 bytes, checksum: 03728fa2f3ef21149ad9c1b4e45c720b (MD5)
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Our goal in this work is to present a theorem which characterizes the gradient solitons rigid for non-compact case. As an application we prove that the homogeneous gradient solitons are rigid and provide an example of the Ricci soliton can not be gradient.
Nosso objetivo nesse trabalho é apresentar um teorema que caracteriza os solitons gradiente rígidos para caso não compacto. Como aplicação provaremos que os solitons gradiente homogêneos são rígidos e apresentaremos um exemplar de soliton de Ricci que não pode ser gradiente.
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Grün, Marc. "Analyse de la dynamique de solitons photoréfractifs". Metz, 2007. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/2007/Grun.Marc.SMZ0703.pdf.
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Les faisceaux laser se propageant dans un cristal photoréfractif sont à l'origine de la formation de solitons spatiaux nommés solitons photoréfractifs, dans le cadre d'un phénomène nommé filamentation. Leur dynamique complexe et sensible aux conditions initiales suggère la présence d'un chaos spatial, pressenti par les simulations numériques de propagation de faisceau. De manière à caractériser ce supposé chaos, nous utilisons d'abord un programme de modélisation basé sur une interprétation système des solitons ; la méthode de conformations d'événements quantifie alors la divergence entre deux dynamiques issues de populations de solitons très proches. La plupart des résultats montrent une décorrélation rapide ; mais la dynamique ainsi modélisée ne peut pas être qualifiée de chaotique étant donnée sa dégradation tendancielle. Revenant aux simulations, nous construisons dans le cadre d'une approche statistique des estimateurs nommés forces de complexité quantifiant la divergence entre deux simulations ; ceux-ci s'avèrent être directement proportionnels au coefficient non-linéaire, un paramètre physique du cristal simulé. Une identique dégradation de la dynamique empêche celle-ci d'être identifiée à un chaos ; néanmoins, elle esquisse une pareille sensibilité aux conditions initiales. Cette méthode est ensuite adaptée à des données expérimentales, où la décorrélation dans le temps et l’espace a pu être quantifiée avec succès grâce à un concept nouveau de multicorrélation. Puis utilisant des concepts de dimension fractale et d'estimateurs issus de l'économétrie, nous avons caractérisé comment s'organise des points de vue nodal et redistribution de l'énergie la dynamique solitonique. Enfin, nous avons conclu qu'en dépit d'une absence de validation rigoureuse de certains critères de chaos, la dynamique présente une forte décorrélation dont les caractérisations quantitatives montrent une analogie empirique avec un système chaotiqueLaser beams propagating in a photorefractive crystal create spatial solitons called photorefractive solitons, in a phenomenon labelled filamentation. Their dynamics, complex and sensitive to initial conditions, make us assume the presence of spatial chaos, as would suggest beam propagation simulations. In order to characterize this assumed chaos, we first used a Modelling Program based upon a system interpretation of solitons ; Event Conformation Method then quantized the divergence between two dynamics from near but different solitons populations. Most results showed fast decorrelations ; but the dynamics we thus characterized cannot be labelled chaotic, because of their tendency to decay. Coming back to simulations, we built statistical estimators called ‘divergence strengths’ quantizing the divergence between two simulations ; these estimators show to be proportional to nonlinear coefficient, a parameter of the modelled crystal. Because of an identical decay, these dynamics cannot be qualified as chaotic ; nevertheless, the high initial condition sensitiveness is on par with a chaotic system. This method was then adapted to experimental data, where time and space decorrelation has been successfully characterized thanks to an innovative concept of multicorrelation. Then, using concepts based on fractal dimensions and estimators from econometrics, we characterized the organizing of solitons dynamics, node-wise and energy redistribution-wise. Thus we concluded that despite the absence of validation of a few chaos criteria, dynamics there show strong decorrelations whose numerical characterizations display empirical resemblance to a standard chaotic system
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Pickartz, Sabrina. "All-optical control of fiber solitons". Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19468.
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Das Thema dieser Arbeit ist eine mögliche Steuerung eines optischen Solitons in nichtlinearen optischen Fasern. Es gelang, die interessierenden Solitonparameter wie Intensität, Dauer und Zeitverschiebung durch die Wechselwirkung mit einer dispersiven Welle geringer Intensität kontrollierbar zu modifizieren.
Es wird eine neue analytische Theorie vorgestellt für die Wechselwirkung zwischen Solitonen und dispersiven Wellen, die auf der Kreuzphasenmodulation in nichtlinearen Fasern beruht. Das vorgestellte Modell kombiniert quantenmechnische Streutheorie und eine Erweiterung der Störungstheorie für Solitonen aus der nichtlinearen Optik. Damit wurden folgende neue Ergebnisse erzielt: (1) Die Entwicklung aller Solitonparameter wird korrekt vorhergesagt. Insbesondere wird die mögliche Verstärkung der Solitonamplitude erfolgreich bestimmt. (2) Passende Intervalle der Kontrollparameter, die eine effektive Solitonmanipulation garantieren, können quantitativ bestimmt werden. (3) Der Raman-Effekt wurde in die Modellbeschreibung eingebunden. Die klassische Abschätzung der Eigenfrequenzverschiebung des Solitons durch den Raman-Effekt wurde verbessert und erweitert durch eine neue Relation für den einhergehenden Amplitudenverlust. Weiterhin wurden solche Kontrollpulse bestimmt, die dieser Schwächung des Solitons entgegenwirken. Im Unterschied zu früheren Versuchen liefert die hier entwickelte Modellbeschreibung die passenden Parameterbereiche für eine stabile Auslöschung des Raman-Effektes. (4) Obwohl die Wechselwirkung selbst auf der Kreuzphasenmodulation basiert, spielt der ”self-steepening“- Effekt, der die Bildung von optischen Schocks beschreibt, eine entscheidende Rolle für eine effiziente Veränderung der Solitonparameter.This work discusses the problem how to control an optical soliton propagating along a non- linear fiber. The approach chosen here is to change soliton delay, duration and intensity in a simple, predictable manner by applying low-intensity velocity-matched dispersive light waves. A new analytic theory of cross-phase modulation interactions of solitons with dispersive control waves is presented which combines quantum mechanical scattering theory, a modified soliton perturbation theory and a multi-scale approach. This led to the following new results: (1) The evolution of all soliton parameters is correctly predicted. In particular the possible amplitude enhancement of solitons is successfully quantified, which could not be obtained by the standard formulation of the soliton perturbation theory. (2) General ranges for control parameters are quantitatively determined, which ensure an effective interaction. (3) The Raman effect is incorporated into the theory. The classical estimation of the Raman self-frequency shift is refined and expanded by a new relation for the amplitude loss arising with the Raman self-frequency shift. Furthermore, control pulses are identified which cancel soliton degradation due to Raman effect. In contrast to previously reported attempts with the interaction scheme under consideration, even parameter ranges are found which lead to a stable cancellation of the Raman effect. (4) New qualitative insights into the underlying process emerged. The prominent role of the self-steepening effect could be isolated. Though the pulse interaction is mediated by cross-phase modulation, the self-steepening effect causes an essential enhancement leading to much stronger changes in soliton parameters.
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Hashimoto, Koji. "New Solitons from Brane Configurations". 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/181110.
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Elias, Ricardo. "Solitons magnétiques et transitions topologiques". Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4712/document.
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Dans cette thèse nous étudions théoriquement et numériquement les solitons magnétiques et leurs transitions topologiques. Dans une première partie, nous trouvons une solution en 3 dimensions appelée Point de Bloch qui vient de la minimisation de l'énergie d'échange, de l'énergie de Landau et de l'énergie dipolaire. Les oscillations autour du point de Bloch sont trouvées et quantifiées pour étudier le rôle des fluctuations quantiques dans sa stabilité.Dans une deuxième partie, nous regardons l'évolution d'un système ferromagnétique avec des textures de topologie non-triviale, couplé à des électrons itinérants qui interagissent avec la texture au moyen de leurs spins. Ce système physique est modelé avec l'équation de Landau-Lifshitz-Gilbert couplée à l'équation de Schrödinger des électrons quantiques. Des transitions topologiques sont observées et mises dans un cadre général. De la grande quantité des transitions topologiques observées, nous distinguons les différents rôles que jouent les électrons selon le régime et l'ensemble de paramètres. Les ordres de grandeur temporels et spatiales des transitions topologiques montrent l'importance des effets quantiques ainsi que des effets de discrétisation du problèmeIn this thesis we study the magnetic solitons and its topological transitions, both theoretically and numerically. In the first part, we find a particular configuration of what is denominated the Bloch Point, a three-dimensional solution of the Free Energy minimization with exchange, Landau and dipolar terms. Oscillations around the Bloch point are found and quantized in order to understand the role of quantum fluctuations over its stability.In the second part, we look at the evolution of a system coupling ferromagnetic textures with nontrivial topology, with itinerant electrons. The interaction between the magnetic texture and the electrons is understood by means of spin-torque phenomena. This physical system is modeled with the equation Landau-Lifshitz-Gilbert equation coupled with Schrödinger equation for quantum electrons. Topological transitions are observed and understood in a general framework that unifies older works done in a more classical context. Among the large amount of topological transitions observed, we can distinguish the different roles played by electrons depending on parameters. The orders of magnitude of time and space in the topological transition events show the importance of quantum effects as well as the fundamental role of discretization
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Gillard, Mike. "Solitons and volume preserving flow". Thesis, Durham University, 2010. http://etheses.dur.ac.uk/533/.
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Solitons arise as solutions to non-linear partial differential equations. These equations are only analytically solvable in very few special cases. Other solutions must be found numerically. A useful technique for obtaining static solutions is gradient flow. Gradient flow evolution is in a direction which never increases energy, leading to solutions which are local minima. Here, a modified version of gradient flow referred to as volume preserving flow is introduced. This flow is constructed to evolve solutions towards local minima, while leaving a number of global quantities unaltered. Volume preserving gradient flow will be introduced and demonstrated in some simple models. Volume preserving flow will be used to investigate minimal surfaces in the context of double bubbles. Work will reproduce explicit results for double bubbles on the two-torus and construct a range of possible minimisers on the three-torus. Domain walls in a Wess-Zumino model with a triply degenerate vacuum will be used to represent the surfaces of the bubbles. Volume preserving flow will minimise the energy of the domain walls while maintaining the volumes of the space they contain. Global minima will represent minimal surfaces in the limit in which the domain wall thickness tends to zero. Numerical simulations of solitons in models which have conformal symmetry are problematic. Discretisation breaks the zero modes associated with changes of scale to negative modes. These lead to the collapse of solutions. Volume preserving flow provides a framework in which minimisation occurs orthogonally to these zero modes, maintaining a scale for the minimisation. Two such conformal models which permit Hopf solitons are the Nicole and AFZ models. They are comprised of the two components of the Skyrme-Faddeev model, taken to fractional powers to allow for solitons. Volume preserving flow will be used to find static solutions for a range of Hopf charges for each model. Comparisons will be made with the Skyrme-Faddeev model and general features of Hopf solitons will be discussed. A one parameter family of conformal Skyrme-Faddeev models will also be introduced. These models will be the set of linear combinations of the Nicole and AFZ models where the coefficients sum to one. Energy and topology transitions through this set of models will be investigated.
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Makris, Konstantinos. "OPTICAL SOLITONS IN PERIODIC STRUCTURES". Doctoral diss., University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4118.
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By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.Ph.D.
Optics and Photonics
Optics and Photonics
Optics PhD
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Lai, Yinchieh. "Quantum theory of optical solitons". Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42512.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1991.Includes bibliographical references (leaves 93-98).
v by Yinchieh Lai.
Ph.D.
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Long, Eamonn. "On charged solitons and electromagnetism". Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614274.
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Plansangkate, Prim. "Anti-self-duality and solitons". Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611695.
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Gutowski, Jan Bernard. "Black holes and brane solitons". Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620991.
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Collie, Benjamin Paul. "Dynamics and structure of solitons". Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608391.
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Westmoreland, Shawn Michael. "Optical black holes and solitons". Diss., Kansas State University, 2010. http://hdl.handle.net/2097/6910.
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Doctor of PhilosophyDepartment of Mathematics
Louis Crane
We exhibit a static, cylindrically symmetric, exact solution to the Euler-Heisenberg field equations (EHFE) and prove that its effective geometry contains (optical) black holes. It is conjectured that there are also soliton solutions to the EHFE which contain black hole geometries.
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Veras, Diego Frankin de Souza. "Solitons em macromolÃculas polimÃricas helicoidais". Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=8887.
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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgicoUm dos desafios da FÃsica TeÃrica à a tentativa de explorar como seus conceitos e tÃcnicas podem ser aplicados à Biologia para descrever a dinÃmica da matÃria viva. A complexidade da estrutura e organizaÃÃo dos sistemas biolÃgicos conduz a efeitos nÃo-lineares onde à possÃvel a manifestaÃÃo de mecanismos solitÃnicos. Uma forma atrativa de se estudar a propagaÃÃo de energia vibracional em biopolÃmeros, tais como proteÃnas, à baseada em modelos de redes nÃo-lineares. Na dÃcada de 1970, Davidov sugeriu que os modos de vibraÃÃes intramoleculares de uma proteÃna estÃo relacionados Ãs interaÃÃes presentes nas deformaÃÃes de sua estrutura e propagam ao longo da cadeia polipeptÃdica com velocidade constante. Este à um comportamento de ondas solitÃrias (soluÃÃes de certas classes de equaÃÃes de onda nÃo-lineares). Os modelos bÃsicos utilizados para se estudar a dinÃmica nÃo linear de macromolÃculas polimÃricas trabalham com redes anarmÃnicas unidimensionais. No entanto, tais molÃculas sÃo tridimensionais e à necessÃrio levar em conta nÃo apenas deslocamentos longitudinais mas tambÃm deslocamentos transversais à cadeia. Com base no fato de que, no estado fundamental, uma macromolÃcula polimÃrica assume a forma de uma hÃlice, estudamos um modelo fÃsico que descreve a dinÃmica nÃo linear de polÃmeros, em particular, para uma proteÃna alfa-hÃlice, tratando com interaÃÃes entre monÃmeros de diferentes ciclos da hÃlice, responsÃveis por estabilizar a geometria espiral da molÃcula. As soluÃÃes numÃricas das equaÃÃes dinÃmicas obtidas para esta cadeia mostram que o modelo suporta soluÃÃes do tipo sÃliton. Analizamos ainda quais os valores aceitÃveis dos parÃmetros livres para que estas soluÃÃes existam. Mostramos de que forma os sÃlitons representam uma torÃÃo na molÃcula e como suas dinÃmicas descrevem a propagaÃÃo desta torÃÃo ao longo da cadeia protÃica.
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Fogaça, David Augaitis. "Solitons em colisões núcleon-núcleo". Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-24032009-003904/.
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Supondo que o núcleo possa ser tratado como um fluido perfeito, nós estudamos as condições para a formação de solitons de Korteweg-de Vries (KdV) na matéria nuclear. A existência de solitons de KdV depende da equação de estado nuclear que, por sua vez, depende da teoria microcóspica subjacente da interação núcleon-núcleon e das aproximações feitas durante os cálculos. No nosso trabalho, nós retomamos estudos sobre solitons no núcleo feitos no passado e substituímos a equação de estado usada anteriormente por outra mais moderna e mais realista, baseada no modelo de Walecka e suas variantes. Nossa análise mostra que solitons de KdV podem ser formados no interior do núcleo com largura em torno de um a dois fermis.Assuming that the nucleus can be treated as a perfect fluid we study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. The existence of these solitons depends on the nuclear equation of state, which, in its turn, depends on the underlying microscopic theory of the nucleon-nucleon interaction and also on the approximations used in the calculations. In this work we reexamine early works on nuclear solitons, replacing the old equations of state by others, more modern and more realistic, base on QHD and on its variants. Our analysis shows that KdV solitons may indeed be formed in the nucleus with a width around one and two fermis.
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Micciche, Salvatore. "Physical properties of gravitational solitons". Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/33196.
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Soliton solutions of Einstein's field equations for space–times with two non-null, commuting Killing Vectors are exact solutions obtained using the solution-generating techniques that resemble the well-known Inverse Scattering Methods that have been widely used m the solution of certain nonlinear PDE's such as Korteweg–de Vries, Sine–Gordon, non-linear Schrödinger. There exist two main soliton techniques in General Relativity. The Belinski–Zakharov technique allows for purely gravitational solutions. The Alekseev technique allows for solutions of the Einstein–Maxwell equations. In both techniques, solitons arise in connection with the poles of a certain so-called "dressing matrix".
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Allen, Michael A. "The evolution of plane solitons". Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/107575/.
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In this work we use the Zakharov-Kuznetsov equation to study the evolution of a plane soliton subjected to a two-dimensional perturbation. The first part of the thesis is concerned with determining the growth rate of such a perturbation. We present two closely related methods which allow us to obtain rigorously the growth rates much more directly and simply than previous approaches. Both methods are general and hence applicable to other problems. If the perturbation is of a large enough wavelength, the plane soliton will evolve into more stable coherent structures of the form of two-dimensional solitons. This process is the subject of the remainder of the thesis. A weakly nonlinear analysis which fully describes the preliminary stages of the process is developed. We have studied how the eventual fate of a plane soliton is affected by the wavelength of the perturbation and obtained a simple formula for the variation of the number of cylindrical solitons formed with this wavelength. The methods developed in this thesis have been used to obtain an analytical description of a soliton state that occurs in coupled optical fibres.
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Weir, David J. "Quantum mechanics of topological solitons". Thesis, Imperial College London, 2011. http://hdl.handle.net/10044/1/9146.
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Topological solitons - are of broad interest in physics. They are objects with localised energy and stability ensured by their topological properties. It is possible to create them during phase transitions which break some sym- metry in a frustrated system. They are ubiquitous in condensed matter, ranging from monopole excitations in spin ices to vortices in superconduc- tors. In such situations, their behaviour has been extensively studied. Less well understood and yet equally interesting are the symmetry-breaking phase transitions that could produce topological defects is the early universe. Grand unified theories generically admit the creation of cosmic strings and monopoles, amongst other objects. There is no reason to expect that the behaviour of such objects should be classical or, indeed, supersymmetric, so to fully understand the behaviour of these theories it is necessary to study the quantum properties of the associated topological defects. Unfortunately, the standard analytical tools for studying quantum field theory - including perturbation theory - do not work so well when applied to topological defects. Motivated by this realisation, this thesis presents numerical techniques for the study of topological solitons in quantum field theory. Calculations are carried out nonperturbatively within the framework of lattice Monte Carlo simulations. Methods are demonstrated which use correlation functions to study the mass, interaction form factors, dispersion relations and excitations of quantum topological solitons. Results are compared to exact expressions obtained from integrability, and to previous work using less sophisticated numerical techniques. The techniques developed are applied to the prototypical kink soliton and to the 't Hooft-Polyakov monopole.
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Söhn, Matthias. "Solitons in Bose-Einstein Condensates". [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10047894.
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Carr, Lincoln D. "Solitons in Bose-Einstein condensates /". Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/9702.
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Watanabe, Kimitaka. "Quantum effects in optical solitons /". Electronic version of summary, 1993. http://www.wul.waseda.ac.jp/gakui/gaiyo/1942.pdf.
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Muhamed, Abera Ayalew. "Moduli spaces of topological solitons". Thesis, University of Kent, 2015. https://kar.kent.ac.uk/47961/.
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This thesis presents a detailed study of phenomena related to topological solitons (in $2$-dimensions). Topological solitons are smooth, localised, finite energy solutions in non-linear field theories. The problems are about the moduli spaces of lumps in the projective plane and vortices on compact Riemann surfaces. Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions in real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge $3$ lumps is a $7$- dimensional manifold of cohomogeneity one. In this thesis, we discuss the charge $3$ moduli space, calculate its metric and find explicit formula for various geometric quantities. We discuss the moment of inertia (or angular integral) of moduli spaces of charge $3$ lumps. We also discuss the implications for lump decay. We discuss interesting families of moduli spaces of charge $5$ lumps using the symmetry property and Riemann-Hurwitz formula. We discuss the K\"ahler potential for lumps and find an explicit formula on the $1$-dimensional charge $3$ lumps. The metric on the moduli spaces of vortices on compact Riemann surfaces where the fields have zeros of positive multiplicity is evaluated. We calculate the metric, K\"{a}hler potential and scalar curvature on the moduli spaces of hyperbolic $3$- and some submanifolds of $4$-vortices. We construct collinear hyperbolic $3$- and $4$-vortices and derive explicit formula of their corresponding metrics. We find interesting subspaces in both $3$- and $4$-vortices on the hyperbolic plane and find an explicit formula for their respective metrics and scalar curvatures. We first investigate the metric on the totally geodesic submanifold $\Sigma_{n,m},\, n+m=N$ of the moduli space $M_N$ of hyperbolic $N$-vortices. In this thesis, we discuss the K\"{a}hler potential on $\Sigma_{n,m}$ and an explicit formula shall be derived in three different approaches. The first is using the direct definition of K\"ahler potential. The second is based on the regularized action in Liouville theory. The third method is applying a scaling argument. All the three methods give the same result. We discuss the geometry of $\Sigma_{n,m}$, in particular when $n=m=2$ and $m=n-1$. We evaluate the vortex scattering angle-impact parameter relation and discuss the $\frac{\pi}{2}$ vortex scattering of the space $\Sigma_{2,2}$. Moreover, we study the $\frac{\pi}{n}$ vortex scattering of the space $\Sigma_{n,n-1}$. We also compute the scalar curvature of $\Sigma_{n,m}$. Finally, we discuss vortices with impurities and calculate explicit metrics in the presence of impurities.
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Ashcroft, Jennifer. "Topological solitons and their dynamics". Thesis, University of Kent, 2017. https://kar.kent.ac.uk/64633/.
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Topological solitons are particle-like solutions of nonlinear field equations with important applications in physics. This thesis presents four research projects concerning topological solitons and their dynamics. We investigate solitons in (1+1)- and (2+1)-dimensions, and develop numerical methods to obtain static solutions and simulate soliton scattering. We first study kink collisions in a model with two scalar fields in the presence of false vacua. We find a variety of scattering outcomes depending on the initial velocity and vacuum structure. Kinks can either repel, form a true or false domain wall, annihilate, or collide and escape to infinity. These behaviours occur in alternating windows of initial velocity. When the kinks escape to infinity, there are a number of oscillations or 'bounces' before the kinks escape, and this bounce number is conserved in each of the windows. In the second project we design new baby Skyrme models that do not require a potential term to allow topological soliton solutions. We raise the Skyrme and sigma terms to fractional powers, which enables us to evade Derrick's theorem. We calculate topological energy bounds for our models and numerically obtain minimal energy solutions for solitons of charge 1, 2, and 3. For each charge, the minimal energy solution is a ring. The last two projects concern vortices in the Ginzburg-Landau model. In the first of these, we numerically investigate the scattering of multi-vortex rings. When two 2-vortex rings collide, there are two distinct scattering outcomes. In both cases, one pair of vortices will scatter at right angles and escape along the y-axis. The remaining two vortices will either form a bound state or escape along an axis after colliding a number of times. Finally, we study vortices scattering with magnetic impurities of the form σ(r)=ce-dr2 An impurity will attract or repel a vortex depending on the coupling constant λ and the parameters c and d. We scatter critically coupled vortices with two different impurities and explore the relationship between the scattering angle and impact parameter. We also find that a 2-vortex ring will break up in a head-on collision with an impurity.
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Wink, Matthias. "Ricci solitons and geometric analysis". Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.
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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an alternative construction of non-compact Einstein metrics of non-positive scalar curvature due to Böhm. It is explained how the asymptotics of the Ricci flat trajectories induce Böhm's Einstein metrics on spheres and other low dimensional spaces. A numerical study suggests that all other Einstein metrics of positive scalar curvature which are induced by the generalised Hopf fibrations occur in an entirely non-linear regime of the Einstein equations. Extending the theory of cohomogeneity one steady and expanding Ricci solitons, an estimate which allows to prescribe the growth rate of the soliton potential at any given time is shown. As an application, continuous families of Ricci solitons on complex line bundles over products of Fano Kähler Einstein manifolds are constructed. This generalises work of Appleton and Stolarski. The method also applies to the Lü-Page-Pope set-up and allows to cover an optimal parameter range in the two summands case. The Ricci soliton equation on manifolds foliated by torus bundles over products of Fano Kähler Einstein manifolds is discussed. A rigidity theorem is obtained and a preserved curvature condition is discovered. The cohomogeneity one initial value problem is solved for m-quasi-Einstein metrics and complete metrics are described. Lp-Poincaré inequalities for k-differentials on closed Riemann surfaces are shown. The estimates are uniform in the sense that the Poincaré constant only depends on p ≥1, k ≥ 2 and the genus γ ≥ 2 of the surface but not on its complex structure. Examples show that the analogous estimate for 1-differentials cannot be uniform. This part is based on joint work with Melanie Rupflin.
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Veras, Diego Frankin de Souza. "Solitons em macromoléculas poliméricas helicoidais". reponame:Repositório Institucional da UFC, 2012. http://www.repositorio.ufc.br/handle/riufc/13678.
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VERAS, Diego Frankin de Souza. Solitons em macromoléculas poliméricas helicoidais. 2012. 79 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2012.Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-20T20:11:29Z No. of bitstreams: 1 2012_dis_dfsveras.pdf: 1461424 bytes, checksum: e03cd018aa0d13ccd561b6569912d54e (MD5)
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Made available in DSpace on 2015-10-21T20:39:53Z (GMT). No. of bitstreams: 1 2012_dis_dfsveras.pdf: 1461424 bytes, checksum: e03cd018aa0d13ccd561b6569912d54e (MD5) Previous issue date: 2012
Um dos desafios da Física Teórica é a tentativa de explorar como seus conceitos e técnicas podem ser aplicados à Biologia para descrever a dinâmica da matéria viva. A complexidade da estrutura e organização dos sistemas biológicos conduz a efeitos não-lineares onde é possível a manifestação de mecanismos solitônicos. Uma forma atrativa de se estudar a propagação de energia vibracional em biopolímeros, tais como proteínas, é baseada em modelos de redes não-lineares. Na década de 1970, Davidov sugeriu que os modos de vibrações intramoleculares de uma proteína estão relacionados às interações presentes nas deformações de sua estrutura e propagam ao longo da cadeia polipeptídica com velocidade constante. Este é um comportamento de ondas solitárias (soluções de certas classes de equações de onda não-lineares). Os modelos básicos utilizados para se estudar a dinâmica não linear de macromoléculas poliméricas trabalham com redes anarmônicas unidimensionais. No entanto, tais moléculas são tridimensionais e é necessário levar em conta não apenas deslocamentos longitudinais mas também deslocamentos transversais à cadeia. Com base no fato de que, no estado fundamental, uma macromolécula polimérica assume a forma de uma hélice, estudamos um modelo físico que descreve a dinâmica não linear de polímeros, em particular, para uma proteína alfa-hélice, tratando com interações entre monômeros de diferentes ciclos da hélice, responsáveis por estabilizar a geometria espiral da molécula. As soluções numéricas das equações dinâmicas obtidas para esta cadeia mostram que o modelo suporta soluções do tipo sóliton. Analizamos ainda quais os valores aceitáveis dos parâmetros livres para que estas soluções existam. Mostramos de que forma os sólitons representam uma torção na molécula e como suas dinâmicas descrevem a propagação desta torção ao longo da cadeia protéica.
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Junior, Ernani de Sousa Ribeiro. "A geometria das mÃtricas tipo-Einstein". Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6655.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorConselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
O objetivo deste trabalho à estudar a geometria das mÃtricas tipo-Einstein (solitons de Ricci, quase solitons de Ricci e mÃtricas quasi-Einstein). Mais especificamente, vamos obter equaÃÃes de estrutura, exemplos, fÃrmulas integrais e estimativas que permitirÃo caracterizar estas classes de mÃtricas.
The purpose of this work is study the geometric of the like-Einstein metrics (Ricci soliton, almost Ricci solitons and quasi-Einstein metrics). More specifically, we obtain structure equations, examples, integral formulae and estimates that will enable characterize these classes of metrics.
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Mak, William Chi Keung Electrical Engineering & Telecommunications Faculty of Engineering UNSW. "Coupled Solitary Waves in Optical Waveguides". Awarded by:University of New South Wales. Electrical Engineering and Telecommunications, 1998. http://handle.unsw.edu.au/1959.4/17494.
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Soliton states in three coupled optical waveguide systems were studied: two linearly coupled waveguides with quadratic nonlinearity, two linearly coupled waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear waveguide with resonant gratings, which enable three-wave interaction. The methods adopted to tackle the problems were both analytical and numerical. The analytical method mainly made use of the variational approximation. Since no exact analytical method is available to find solutions for the waveguide systems under study, the variational approach was proved to be very useful to find accurate approximations. Numerically, the shooting method and the relaxation method were used. The numerical results verified the results obtained analytically. New asymmetric soliton states were discovered for the coupled quadratically nonlinear waveguides, and for the coupled waveguides with both cubic nonlinearity and Bragg gratings. Stability of the soliton states was studied numerically, using the Beam Propagation Method. Asymmetric couplers with quadratic nonlinearity were also studied. The bifurcation diagrams for the asymmetric couplers were those unfolded from the corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound states due to three-wave interaction were discovered for a quadratically nonlinear waveguide equipped with resonant gratings. Since the coupled optical waveguide systems are controlled by a larger number of parameters than in the corresponding single waveguide, the coupled systems can find a much broader field of applications. This study provides useful background information to support these applications.
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Santos, Blanco María Concepción. "Optical solitons in quadratic nonlinear media and applications to all-optical switching and routing devices". Doctoral thesis, Universitat Politècnica de Catalunya, 1998. http://hdl.handle.net/10803/6913.
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Esta tesis constituye un estudio detallado y exhaustivo de las propiedades de una variedad específica de ondas ópticas solitarias. Observadas experimentalmente por primera vez en 1995, estas ondas estan formadas por un haz óptico a frecuencia fundamental y su segundo armónico que están ligados entre sí y viajan juntos en el material cuadrático; y son debidas al equilibrio entre la difracción lineal que sufre el haz al propagarse y un término no lineal de segundo orden en la susceptibilidad del medio. Las llamamos por eso solitones ópticos en medios cuadráticos o simplemente 'solitones cuadráticos'. También se les conoce como 'Solitones Multicolor' aludiendo al hecho de que requieren de haces a diferentes frecuencias para formarse.Un medio no-lineal cuadrático tiene por fuerza que ser no-centrosimétrico, lo cual es una variedad de anisotropía. Una gran parte de los materiales no-lineales cuadráticos (los que tienen mayor interés para la industria) son uniaxiales lo que significa que presentan un eje de simetría que suele llamarse eje óptico. De la dirección de un haz relativa a ese eje óptico dependen las características de la propagación del haz en el medio cuadrático no-lineal. Una consecuencia de eso en configuraciones de interés es un desvío ('walk-off') sufrido por el haz respecto a su dirección de propagación inicial al entrar en el material no-lineal.
Las propiedades de los solitones cuadráticos 'caminantes' son también estudiadas en la tesis, estableciendo que existe una relación entre la potencia inyectada en el medio y el ángulo de desvío (walking angle).
Una parte importante de la tesis está dedicada al estudio a través de exhaustivos experimentos numéricos del potencial de estas ondas solitarias para constituir la base de dispositivos de conmutación y encaminamiento totalmente ópticos que puedan hacer realidad la promesa de la red transparente totalmente óptica. Los experimentos han permitido identificar varias configuraciones de interés con niveles de potencia y dimensiones que permiten plantearse el diseño y construcción de dispositivos comerciales de conmutación y encaminamiento totalmente ópticos basados en solitones ópticos cuadráticos.
This thesis is a comprehensive study of the fundamental properties of a specific kind of optical spatial solitary waves. First observed experimentally in 1995, these solitary waves are formed by an optical beam at a fundamental frequency and its second harmonic which propagate together and are mutually entangled; and are due to a balanced interplay between the beams' linear diffraction and a second-order nonlinear susceptibility of the medium. They are thereby referred as 'Optical Solitons in Quadratic Nonlinear Media' or simply 'Quadratic Solitons', They are also known as 'Multicolor Solitons' recalling that they are formed by beams at different frequencies.
A quadratic nonlinear media needs to be non centrosymmetric which is a special kind of anisotropy. A great deal of quadratic nonlinear materials (the most used by industry such as lithim niobate, KTP, etc.) are uniaxial meaning that they feature a symmetry axis known as 'optical axis'. The direction of propagation of an optical beam relative to that axis determines the characteristics of the beam's propagation through the quadratic nonlinear material. A main result of that in some configurations of interest is a walk-off suffered by the beam as it enters the quadratic material.
The properties of the families of quadratic solitons in the presence of a linear walk-off (quadratic walking solitons) are studied as well in the thesis stating that there is a relationship between the power injected into the medium and the walking angle, suitable to applications of all-optical switching and routing.
An important last part of the thesis is devoted to the study from a practical viewpoint and through extensive numerical experiments of the potential of these solitary waves as the basis of practical all-optical switches and routers which could take the all-optical transparent network to a reality. The experiments have allowed to identify several configurations of interest with power level and dimensions suited to practical applications which could allow the production of commercial all-optical switching and routing devices based on quadratic solitons.
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Xiong, Xiaozhen. "Noncommutative field theories, solitons and superalgebra". [Gainesville, Fla.]: University of Florida, 2002. http://purl.fcla.edu/fcla/etd/UFE0000620.
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Genevet, Patrice. "Laser à solitons et vortex localisés". Phd thesis, Université de Nice Sophia-Antipolis, 2009. http://tel.archives-ouvertes.fr/tel-00435984.
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Les solitons de cavité (SC) sont des structures spatiales localisées que l'on peut générer dans une cavité optique non-linéaire. Ces structures se présentent sous la forme de pics lumineux de sur-intensité, "posées" sur un fond de lumière homogène. Depuis leur découverte, de nombreuses démonstrations de principe ont été réalisées, mettant en évidence leurs utilisations pour le traitement tout optique de l'information. Néanmoins, l'implémentation de dispositifs capables de générer des solitons de cavité dans le réseau télécom reste à l'heure actuelle improbable. Une simplification mais surtout une miniaturisation, qui passe par l'invention de nouveaux dispositifs, est un objectif majeur de la recherche sur les SC. L'objectif de cette thèse est de montrer qu'un système simple, miniaturisable, appelé Laser à solitons de cavité, permet d'obtenir ce type de structures spatiales localisées. Ce dispositif est obtenu en couplant mutuellement deux lasers de large section transverse. L'un des lasers joue le rôle d'un amplificateur alors que le second sert d'absorbant saturable fournissant le mécanisme de bistabilité. Les structures spatiales localisées obtenues sont indépendamment contrôlables à l'aide d'un faisceau dit d'écriture. La différence fondamentale entre les SCs obtenus avec un laser à SC et les SCs obtenus auparavant est due à la symétrie de phase du système laser. Cette symétrie de phase nous permet de générer des structures composites dont la phase entre les différents constituants n'est pas identique. Nous avons également observé des structures localisées circulaires possédant un défaut de phase en leur centre. Bien que prédit théoriquement, ce type de structure, appelé vortex optique localisé, n'avait jusqu'alors jamais été observé expérimentalement.
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Kikuchi, Toru. "Relativistic zero-mode dynamics of solitons". 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157758.
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Christian, James Michael. "On the theory of Helmholtz solitons". Thesis, University of Salford, 2006. http://usir.salford.ac.uk/26616/.
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This thesis is concerned with spatial optical solitons in (quasi-two dimensional) planar waveguides, where there is a single longitudinal and (effectively) a single transverse dimension, and whose symmetry the solutions respect consistently. A key feature of Helmholtz soliton theory is that, by recognizing the physical equivalence of the longitudinal and transverse dimensions in uniform media, it can access experimental contexts involving broad, moderately intense beams that propagate and interact at arbitrarily large angles. It thus provides an ideal platform for the systematic generalization of established paraxial results (restricted to applications involving vanishingly-small angles) to the finite-angle domain. Helmholtz soliton theory is expected to play a fundamental role in the design of any futuristic integrated-optic device exploiting the propagation and interaction of spatial soliton beams at oblique angles relative to a reference direction. Exact analytical soliton solutions are derived for a variety of newly-proposed scalar and vector Non-Linear Helmholtz equations. These solutions are valid for a wide variety of media, such as some semiconductors, doped glasses and non-linear polymers. Different types of solution classes have been obtained, including hyperbolic (exponentially localized), algebraic (with power-law asymptotics), amplitude-kink (where the intensity varies monotonically), and spatially-extended (such as trigonometric and cnoidal) waves. Exact analytical solutions have also been obtained in the presence of some higher-order effects - for example, gain/absorption and saturation of the non-linear refractive index. Helmholtz solitons are found to exhibit generic features (such as angular beam broadening), and they reduce to their paraxial counterparts when an appropriate multiple limit (defining rigorously a paraxial beam) is enforced. Each new solution has been tested under a numerical perturbative analysis that examines its stability. Helmholtz solitons have been classified largely as robust attractors, in a non-linear dynamical sense, and this stability is crucial if they are to be exploited successfully in practical applications.
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Kolossovski, Kazimir Mathematics & Statistics Australian Defence Force Academy UNSW. "Parametric solitons due to cubic nonlinearities". Awarded by:University of New South Wales - Australian Defence Force Academy. School of Mathematics and Statistics, 2001. http://handle.unsw.edu.au/1959.4/38711.
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The main subject of this thesis is solitons due to degenerate parametric four-wave mixing. Derivation of the governing equations is carried out for both spatial solitons (slab waveguide) and temporal solitons (optical fibre). Higher-order effects that are ignored in the standard paraxial approximation are discussed and estimated. Detailed analysis of conventional solitons is carried out. This includes discovery of various solitons families, linear stability analysis of fundamental and higher-order solitons, development of theory describing nonlinear dynamics of higher-order solitons. The major findings related to the stationary problem are bifurcation of a two-frequency soliton family from an asymptotic family of infinitely separated one-frequency solitons, jump bifurcation and violation of the bound state principle. Linear stability analysis shows a rich variety of internal modes of the fundamental solitons and existence of a stability window for higher-order solitons. Theory for nonlinear dynamics of higher-order solitons successfully predicts the position and size of the stability window, and various instability scenarios. Equivalence between direct asymptotic approach and invariant based approach is demonstrated. A general analytic approach for description of localised solutions that are in resonance with linear waves (quasi-solitons and embedded solitons) is given. This includes normal form theory and approximation of interacting particles. The main results are an expression for the amplitude of the radiating tail of a quasi-soliton, and a two-fold criterion for existence of embedded solitons. Influence of nonparaxiality on soliton stability is investigated. Stationary instability threshold is derived. The major results are shift and decreasing of the size of the stability window for higher-order solitons. The latter is the first demonstration of the destabilizing influence of nonparaxiality on higher-order solitons. Analysis of different aspects of solitons is based on universal approaches and methods. This includes Hamiltonian formalism, consideration of symmetry properties of the model, development of asymptotic models, construction of perturbation theory, application of general theorems etc. Thus, the results obtained can be extended beyond the particular model of degenerate four-wave mixing. All theoretical predictions are in good agreement with the results of direct numerical modeling.
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Atieh, Ahmad K. "Exploiting solitons in all-optical networks". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ28325.pdf.
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