Letteratura scientifica selezionata sul tema "Boussinesq equation"

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Articoli di riviste sul tema "Boussinesq equation"

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CLARKSON, PETER A. "RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION". Analysis and Applications 06, n. 04 (ottobre 2008): 349–69. http://dx.doi.org/10.1142/s0219530508001250.

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Abstract (sommario):
Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.
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Xu, Fei, Yixian Gao e Weipeng Zhang. "Construction of Analytic Solution for Time-Fractional Boussinesq Equation Using Iterative Method". Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/506140.

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This paper is aimed at constructing analytical solution for both linear and nonlinear time-fractional Boussinesq equations by an iterative method. By the iterative process, we can obtain the analytic solution of the fourth-order time-fractional Boussinesq equation inR,R2, andRn, the sixth-order time-fractional Boussinesq equation, and the2nth-order time-fractional Boussinesq equation inR. Through these examples, it shows that the method is simple and effective.
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Clarkson, Peter A. "New exact solutions of the Boussinesq equation". European Journal of Applied Mathematics 1, n. 3 (settembre 1990): 279–300. http://dx.doi.org/10.1017/s095679250000022x.

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In this paper new exact solutions are derived for the physically and mathematically significant Boussinesq equation. These are obtained in two different ways: first, by generating exact solutions to the ordinary differential equations which arise from (classical and nonclassical) similarity reductions of the Boussinesq equation (these ordinary differential equations are solvable in terms of the first, second and fourth Painlevé equations); and second, by deriving new space-independent similarity reductions of the Boussinesq equation. Extensive sets of exact solutions for both the second and fourth Painlevé equations are also generated. The symbolic manipulation language MACSYMA is employed to facilitate the calculations involved.
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Jafari, Hossein, Nematollah Kadkhoda e Chaudry Massod Khalique. "Application of Lie Symmetry Analysis and Simplest Equation Method for Finding Exact Solutions of Boussinesq Equations". Mathematical Problems in Engineering 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/452576.

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The Lie symmetry approach with simplest equation method is used to construct exact solutions of the bad Boussinesq and good Boussinesq equations. As the simplest equation, we have used the equation of Riccati.
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Fan, Fei, Bing Chen Liang e Xiu Li Lv. "Study of Wave Models of Parabolic Mild Slope Equation and Boussinesq Equation". Applied Mechanics and Materials 204-208 (ottobre 2012): 2334–40. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.2334.

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The Parabolic mild slope equation and Boussinesq equation wave models are studied in this paper. First, the wave models Funwave and REF/DIF, which based on Boussinesq equations and the parabolic mild slope equation, respectively, are introduced. And then, two experiments are used to study these two wave models, one is the non-breaking shoal experiment of University of Delaware and the other is the breaking undertow test experiment, which was finished in Ocean University of China by author. Last, the simulation data of two wave models are compared with the measured data. The results show that both Boussinesq equation and the parabolic mild slope equation wave models can simulated nearshore wave condition precisely, but Boussinesq equation wave models has a disadvantage in catching the variation of wave height caused by wave breaking.
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Bulut, Hasan, Münevver Tuz e Tolga Akturk. "New Multiple Solution to the Boussinesq Equation and the Burgers-Like Equation". Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/952614.

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By considering an improved tanh function method, we found some exact solutions of Boussinesq and Burgers-like equations. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. We found some exact solutions of the Boussinesq equation and the Burgers-like equation.
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Rashidi, Saeede, e S. Reza Hejazi. "Symmetry properties, similarity reduction and exact solutions of fractional Boussinesq equation". International Journal of Geometric Methods in Modern Physics 14, n. 06 (4 maggio 2017): 1750083. http://dx.doi.org/10.1142/s0219887817500839.

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In this paper, some properties of the time fractional Boussinesq equation are presented. Group analysis of the time fractional Boussinesq equation with Riemann–Liouville derivative is performed and the corresponding optimal system of subgroups are determined. Next, we apply the obtained optimal systems for constructing reduced fractional ordinary differential equations (FODEs). Finally, we show how to derive exact solutions to time fractional Boussinesq equation via invariant subspace method.
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Melinand, Benjamin. "Long wave approximation for water waves under a Coriolis forcing and the Ostrovsky equation". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, n. 6 (19 luglio 2018): 1201–37. http://dx.doi.org/10.1017/s0308210518000136.

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This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in one (spatial) dimension and we rigorously justify them as an asymptotic model of water wave equations. These new Boussinesq equations are not the classical Boussinesq equations: a new term due to the vorticity and the Coriolis forcing appears that cannot be neglected. We study the Boussinesq regime and derive and fully justify different asymptotic models when the bottom is flat: a linear equation linked to the Klein–Gordon equation admitting the so-called Poincaré waves; the Ostrovsky equation, which is a generalization of the Korteweg–de Vries (KdV) equation in the presence of a Coriolis forcing, when the rotation is weak; and the KdV equation when the rotation is very weak. Therefore, this work provides the first mathematical justification of the Ostrovsky equation. Finally, we derive a generalization of the Green–Naghdi equations in one spatial dimension for small topography variations and we show that this model is consistent with the water wave equations.
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Johnson, R. S. "A Two-dimensional Boussinesq equation for water waves and some of its solutions". Journal of Fluid Mechanics 323 (25 settembre 1996): 65–78. http://dx.doi.org/10.1017/s0022112096000845.

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A two-dimensional Boussinesq equation, \[u_{tt} - u_{xx} + 3(u^2)_{xx} - u_{xxxx} - u_{yy} = 0,\] is introduced to describe the propagation of gravity waves on the surface of water, in particular the head-on collision of oblique waves. This equation combines the two-way propagation of the classical Boussinesq equation with the (weak) dependence on a second spatial variable, as occurs in the two-dimensional Korteweg-de Vries (2D KdV) (or KPII) equation. Exact and general solitary-wave, two-soliton and resonant solutions are obtained from the Hirota bilinear form of the equation. The existence of a distributed-soliton solution is investigated, but it is shown that this is not a possibility. However the connection with the classical 2D KdV equation (which does possess such a solution) is explored via a suitable parametric representation of the dispersion relation.A three-soliton solution is also constructed, but this exists only if an auxiliary constraint among the six parameters is satisfied; thus the two-dimensional Boussinesq equation is not one of the class of completely integrable equations, confirming the analysis of Hietarinta (1987). This constraint is automatically satisfied for the classical Boussinesq equation (which is completely integrable). Graphical reproductions of some of the solutions of the two-dimensional Boussinesq equations are also presented.
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Abazari, Reza, e Adem Kılıçman. "Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form". Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/468206.

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This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011) and (Kılıcman and Abazari, 2012), that focuses on the application ofG′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientistJoseph Valentin Boussinesq(1842–1929) described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that theG′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
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Tesi sul tema "Boussinesq equation"

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Sitanggang, Khairil Irfan. "Boussinesq-equation and rans hybrid wave model". [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2795.

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Liu, Fang-Lan. "Some asymptotic stability results for the Boussinesq equation". Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40052.

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Sjölander, Filip. "Numerical solutions to the Boussinesq equation and the Korteweg-de Vries equation". Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297544.

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The aim of the report is to numerically construct solutions to two analytically solvable non-linear differential equations: the Korteweg–De Vries equation and the Boussinesq equation. To accomplish this, a range of numerical methods where implemented, including Galerkin methods. To asses the accuracy of the solutions, analytic solutions were derived for reference. Characteristic of both equations is that they support a certain type of wave-solutions called "soliton solutions", which admit an intuitive physical interpretation as solitary traveling waves. Theses solutions are the ones simulated. The solitons are also qualitatively studied in the report.
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Sun, Weizhou. "LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION". The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905.

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Li, Shenghao. "Non-homogeneous Boundary Value Problems for Boussinesq-type Equations". University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1468512590.

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Moore, Kieron R. "Coupled Boussinesq equations and nonlinear waves in layered waveguides". Thesis, Loughborough University, 2013. https://dspace.lboro.ac.uk/2134/13636.

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There exists substantial applications motivating the study of nonlinear longitudinal wave propagation in layered (or laminated) elastic waveguides, in particular within areas related to non-destructive testing, where there is a demand to understand, reinforce, and improve deformation properties of such structures. It has been shown [76] that long longitudinal waves in such structures can be accurately modelled by coupled regularised Boussinesq (cRB) equations, provided the bonding between layers is sufficiently soft. The work in this thesis firstly examines the initial-value problem (IVP) for the system of cRB equations in [76] on the infinite line, for localised or sufficiently rapidly decaying initial conditions. Using asymptotic multiple-scales expansions, a nonsecular weakly nonlinear solution of the IVP is constructed, up to the accuracy of the problem formulation. The asymptotic theory is supported with numerical simulations of the cRB equations. The weakly nonlinear solution for the equivalent IVP for a single regularised Boussinesq equation is then constructed; constituting an extension of the classical d'Alembert's formula for the leading order wave equation. The initial conditions are also extended to allow one to separately specify an O(1) and O(ε) part. Large classes of solutions are derived and several particular examples are explicitly analysed with numerical simulations. The weakly nonlinear solution is then improved by considering the IVP for a single regularised Boussinesq-type equation, in order to further develop the higher order terms in the solution. More specifically, it enables one to now correctly specify the higher order term's time dependence. Numerical simulations of the IVP are compared with several examples to justify the improvement of the solution. Finally an asymptotic procedure is developed to describe the class of radiating solitary wave solutions which exist as solutions to cRB equations under particular regimes of the parameters. The validity of the analytical solution is examined with numerical simulations of the cRB equations. Numerical simulations throughout this work are derived and implemented via developments of several finite difference schemes and pseudo-spectral methods, explained in detail in the appendices.
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Rivas, Ivonne. "Analysis and Control of the Boussinesq and Korteweg-de Vries Equations". University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321371582.

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Hu, Weiwei. "Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems". Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/38664.

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In this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.
Ph. D.
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Attaoui, Abdelatif. "Existence de solutions faibles et faible-renormalisées pour des systèmes non linéaires de Boussinesq". Phd thesis, Université de Rouen, 2007. http://tel.archives-ouvertes.fr/tel-00259252.

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La thèse est consacrée essentiellement à l'étude de systèmes non linéaires d'évolution issus d'un modèle de Boussinesq : couplage entre les équations de Navier-stokes avec un second membre F(µ), où F est une force de gravité proportionnelle à des variations de densité qui dépendent de la température et l'équation de l'énergie.
Le premier chapitre nous donne un résultat d'existence d'une solution faible-renormalisée du système de Boussinesq en dimension 2, dans le cas où F est bornée.
Dans le chapitre 2, on aborde le cas de fonctions F plus générales : F vérifie une hypothèse de croissance. On démontre l'existence de solutions pour toutes données initiales ou pour des données initiales petites selon la croissance de F.
Dans le chapitre 3, nous faisons une généralisation des résultats du chapitre 2 mais sans le terme de convection.
Dans le chapitre 4, le manque de stabilité de l'énergie de dissipation dans L1(Q) en dimension 3, nous contraint à transformer de façon formelle le système de Boussinesq. On démontre l'existence d'une solution faible de ce nouveau système en dimension 3.
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Aldbaissy, Rim. "Discrétisation du problème de couplage instationnaire des équations de Navier-Stokes avec l'équation de la chaleur". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS013.

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Les équations aux dérivées partielles issues de la nature n’ont pas de solutions explicites et ne peuvent de ce fait qu’être résolue de manière approchée. Le travail présenté dans cette thèse porte d’une part sur la résolution du système de Navier-stokes couplé avec l’équation de la température. Ce couplage est connu sous le nom du modèle de Boussinesq. La viscosité et la force extérieure sont non linéaires dépendent de la température. D’autre part, sur la validation numérique des résultats théoriques obtenus dans le cadre académique et industriel. Ce travail porte sur deux parties. Dans la première, nous nous intéressons à l’approximation numérique de la solution des schémas discrets proposés en utilisant la méthode d’Euler semi-implicit pour la dicrétisation en temps et la méthode des éléments finis pour la discrétisation en espace d’ordre un. Dans le but de gagner en temps et en ordre de convergence, nous discrétisons le problème de couplage en ordre deux en temps et en espace, respectivement par la méthode BDF et la méthode des éléments finis d’ordre deux. Nous effectuons ainsi l’analyse de l’erreur a priori des schémas proposés et nous terminons par valider les résultats théoriques déjà obtenus par des simulations numériques en utilisant le logiciel Freefem++. La deuxième partie est dédiée à la modélisation du phénomène bouchon qui apparaît de temps en temps durant l’impression 3D. Dans le but d’améliorer l’algorithme séquentiel 2D et pouvoir passer ensuite à la simulation 3D, nous effectuons des calculs parallèles basés sur la méthode de décomposition de domaine. Les résultats obtenus montrent que cette méthode n’est pas efficace en termes de scalablité. Nous utilisons alors une méthode de préconditionnement à un niveau où les essais numériques décèlent une dépendance de la convergence en fonction du nombre de processeurs et de la physique du modèle. D’où l’idée d’ajouter au préconditionneur un deuxième niveau par la résolution du problème grossier
The analytical solutions of the majority of partial differential equations are difficult to calculate, hence, numerical methods are employed. This work is divided into two parts. First, we study the time dependent Navier-Stokes equations coupled with the heat equation with nonlinear viscosity depending on the temperature known as the Boussinesq (buoyancy) model . Then, numerical experiments are presented to confirm the theoretical accuracy of the discretization using the Freefem++ software. In the first part, we propose first order numerical schemes based on the finite element method for the space discretization and the semi-implicit Euler method for the time discretization. In order to gain time and order of convergence, we study a second order scheme in time and space by using respectively the second order BDF method "Backward Differentiation Formula" and the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Finally, numerical experiments are presented to confirm the theoretical results. The second part is dedicated to the modeling of the thermal instability that appears from time to time while printing using a 3D printer. Our purpose is to build a reliable scheme for the 3D simulation. For this reason, we propose a trivial parallel algorithm based on the domain decomposition method. The numerical results show that this method is not efficient in terms of scalability. Therefore, it is important to use a one-level preconditioning method "ORAS". When using a large number of subdomains, the numerical test shows a slow convergence. In addition, we noticed that the iteration number depends on the physical model. A coarse space correction is required to obtain a better convergence and to be able to model in three dimensions
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Libri sul tema "Boussinesq equation"

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National Aeronautics and Space Administration (NASA) Staff. On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations. Independently Published, 2018.

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A, Babin, e Institute for Computer Applications in Science and Engineering., a cura di. On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Capitoli di libri sul tema "Boussinesq equation"

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Zhang, Bing-Yu. "Exact Controllability of the Generalized Boussinesq Equation". In Control and Estimation of Distributed Parameter Systems, 297–310. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8849-3_23.

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Mothibi, Dimpho Millicent, e Chaudry Masood Khalique. "Exact Solutions of a Coupled Boussinesq Equation". In Springer Proceedings in Mathematics & Statistics, 323–27. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12307-3_46.

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Ascanelli, Alessia, e Chiara Boiti. "Well-Posedness for a Generalized Boussinesq Equation". In Trends in Mathematics, 193–202. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_23.

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Dimova, Milena, e Daniela Vasileva. "Comparison of Two Numerical Approaches to Boussinesq Paradigm Equation". In Lecture Notes in Computer Science, 255–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41515-9_27.

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Porubov, A. V. "On Some Exact Solutions of Hyperbolic Boussinesq Equation with Dissipation". In Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects, 481–86. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-87871-7_58.

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Ludlow, D. K., e P. A. Clarkson. "Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation". In Applications of Analytic and Geometric Methods to Nonlinear Differential Equations, 415–30. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2082-1_40.

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Dimova, Milena, e Natalia Kolkovska. "Comparison of Some Finite Difference Schemes for Boussinesq Paradigm Equation". In Mathematical Modeling and Computational Science, 215–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28212-6_23.

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Kolkovska, Natalia T. "Convergence of Finite Difference Schemes for a Multidimensional Boussinesq Equation". In Numerical Methods and Applications, 469–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18466-6_56.

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Kato, Shouichiro, Akira Anju e Mutsuto Kawahara. "A Finite Element Study of Solitary Wave by Boussinesq Equation". In Computational Methods in Water Resources X, 1067–72. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-010-9204-3_129.

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Vucheva, Veselina, e Natalia Kolkovska. "A Symplectic Numerical Method for the Sixth Order Boussinesq Equation". In Advanced Computing in Industrial Mathematics, 417–27. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71616-5_37.

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Atti di convegni sul tema "Boussinesq equation"

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Choudhury, Jayanta. "2D Solitary Waves of Boussinesq Equation". In ISIS INTERNATIONAL SYMPOSIUM ON INTERDISCIPLINARY SCIENCE. AIP, 2005. http://dx.doi.org/10.1063/1.1900395.

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Vucheva, V., e N. Kolkovska. "A symplectic numerical method for Boussinesq equation". In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 10th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’18. Author(s), 2018. http://dx.doi.org/10.1063/1.5064941.

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Kolkovska, N., e V. Vucheva. "Numerical investigation of sixth order Boussinesq equation". In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’17. Author(s), 2017. http://dx.doi.org/10.1063/1.5007409.

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salmei, H., e F. salimi. "Modified Homotopy Pertutbation Method for solving Boussinesq Equation". In ICMS INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCE. American Institute of Physics, 2010. http://dx.doi.org/10.1063/1.3525215.

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Kudryashov, Nikolay A., e Alexandr K. Volkov. "On analytical solutions of the generalized Boussinesq equation". In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952014.

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Servi, Sema, Yildiray Keskin e Galip Oturanç. "Reduced differential transform method for improved Boussinesq equation". In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912601.

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Anco, S., M. Rosa e M. L. Gandarias. "On conservation laws for a generalized Boussinesq equation". In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992434.

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Kolkovska, N., e V. M. Vassilev. "Solitary waves to Boussinesq equation with linear restoring force". In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5130850.

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BRUGARINO, T., e M. SCIACCA. "SOME EXACT SOLUTIONS OF THE TWO DIMENSIONAL BOUSSINESQ EQUATION". In Proceedings of the 15th Conference on WASCOM 2009. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814317429_0007.

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BRUZÓN, M. S., M. L. GANDARIAS e J. RAMÍREZ. "CLASSICAL SYMMETRIES FOR A BOUSSINESQ EQUATION WITH NONLINEAR DISPERSION". In Proceedings of the International Conference. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812794543_0006.

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Rapporti di organizzazioni sul tema "Boussinesq equation"

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M. A. Jafarizadeh e A. R. Esfandyari. Exact Solutions of Boussinesq Equation. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-304-314.

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Dimova, Milena, Natalia Kolkovska e Nikolay Kutev. Orbital Stability or Instability of Solitary Waves to Generalized Boussinesq Equation with Quadratic-cubic Nonlinearity. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, agosto 2018. http://dx.doi.org/10.7546/crabs.2018.08.01.

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3

Walker, David T. Variational Data Assimilation for Near-Shore Waves Using the Extended Boussinesq Equations. Fort Belvoir, VA: Defense Technical Information Center, ottobre 2005. http://dx.doi.org/10.21236/ada441232.

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