Relevant bibliographies by topics / Integrable

Academic literature on the topic 'Integrable'

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Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Integrable"

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Álvarez Merino, Paula, Carmen Requena Hernández, and Francisco Salto Alemany. "LA INTEGRACIÓN MÁS QUE LA EDAD INFLUYE EN EL RENDIMIENTO DEL RAZONAMIENTO DEDUCTIVO." International Journal of Developmental and Educational Psychology. Revista INFAD de Psicología. 1, no. 2 (October 28, 2016): 221. http://dx.doi.org/10.17060/ijodaep.2016.n2.v1.569.

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Abstract.This work merges from our interest for the evolution of deductive reasoning across the life cycle from youth to older age. With time, reasoning resources seem to be compromised and constrained, even if on the other side they seem more flexible. The literature on deductive reasoning considers that deduction only takes place between integrable premisses, that is, premisses whose elements share any categorematical term. The present research designed, applied and analyzed an instrument to measure deduction. The measure is based on integration as a general rule to deduce a conclusion from two premisses. The internal consistency of the instrument was .775 and its validity was approved by 10 experts. The transversal design had a sample of 37 young and 42 older persons, 12 of which had university degrees. Both young and old groups commit less failures with integrable elements than with non-integrable (p=.000), Importantly, the group of young reasoners show less correct answers differences between integrable and non-integrable inferences. As a conclusion, the high number of deductive errors among older persons in non integrable inferences can be explained because they seem to handle heuristic rules with a low abstraction level, of the kind: “if premisses are not integrable, then the inference is false”. The higher scores obtained by young reasoners with non integrable inferences is eventually explained in terms of the search for subjacent logical reasons in non integrable or even apparently incoherent inferential tasks.Keywords: Deduction, Aging reason, Integrable reasoning, Deductive reasonig measure instrumentResumen.El origen de este trabajo arranca del interés por conocer la evolución del razonamiento deductivo de la juventud a la vejez. Con el tiempo, los recursos razonadores parecen verse comprometidos y limitados, aunque por otra parte pueden aparecer más flexibles. La literatura sobre razonamiento deductivo considera que éste sucede sólo entre premisas que sean integrables. Del concepto de integración no existe una definición precisa aunque hay cierto acuerdo en considerar que son integrables las premisas cuyos elementos comparten algún término categoremático. En la presente investigación se diseño, aplicó y analizó un instrumento para medir la deducción en base a aplicar la integración como regla general entre dos premisas para obtener la conclusión. La consistencia interna del instrumento fue de .775 y la validez de contenido fue aprobada por 10 expertos. El diseño transversal contó con una muestra de 37 jóvones y 42 personas mayores de las que 12 tenían estudios universitarios. El grupo de jóvenes y mayores comenten menos errores en los ítems integrables que en los no integrables (p = .000). Destacablemente, el grupo de jóvenes muestra menor diferencia de aciertos entre inferencias integrables y no integrables. Como conclusión, se explica el amplio número de errores deductivos de mayores en los ítems no integrables porque manejan reglas heurísticas de bajo nivel de abstracción del tipo: si las premisas no son integrables, la inferencia es falsa. El mayor acierto de los jóvenes con inferencias no integrables se explica eventualmente por la búsqueda de razones lógicas subyacentes ante una tarea aparentemente incoherente. Palabras Clave: Deducción, Razonamiento en la vejez, Razonamiento integrable, Razonamiento deductivo instrumento de medida
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Kai, Tatsuya. "Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part II: Foliation Structures and Integrating Algorithms." Mathematical Problems in Engineering 2012 (2012): 1–34. http://dx.doi.org/10.1155/2012/345942.

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This paper investigates foliation structures of configuration manifolds and develops integrating algorithms for a class of constraints that contain the time variable, calledA-rheonomous affine constrains. We first present some preliminaries on theA-rheonomous affine constrains. Next, theoretical analysis on foliation structures of configuration manifolds is done for the respective three cases where theA-rheonomous affine constrains are completely integrable, partially integrable, and completely nonintegrable. We then propose two types of integrating algorithms in order to calculate independent first integrals for completely integrable and partially integrableA-rheonomous affine constrains. Finally, a physical example is illustrated in order to verify the availability of our new results.
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Mañas, Manuel. "From integrable nets to integrable lattices." Journal of Mathematical Physics 43, no. 5 (2002): 2523. http://dx.doi.org/10.1063/1.1454185.

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Maciejewski, Andrzej J., and Maria Przybylska. "Integrable deformations of integrable Hamiltonian systems." Physics Letters A 376, no. 2 (December 2011): 80–93. http://dx.doi.org/10.1016/j.physleta.2011.10.031.

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Xia, Baoqiang, and Ruguang Zhou. "Integrable deformations of integrable symplectic maps." Physics Letters A 373, no. 47 (November 2009): 4360–67. http://dx.doi.org/10.1016/j.physleta.2009.09.063.

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Ning, Wang. "Integrable Bogoliubov Transform and Integrable Model." Chinese Physics Letters 20, no. 2 (January 23, 2003): 177–79. http://dx.doi.org/10.1088/0256-307x/20/2/301.

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ZHU, LI, HONGWEI YANG, and HUANHE DONG. "A LIOUVILLE INTEGRABLE MULTI-COMPONENT INTEGRABLE SYSTEM AND ITS INTEGRABLE COUPLINGS." International Journal of Modern Physics B 24, no. 08 (March 30, 2010): 1021–46. http://dx.doi.org/10.1142/s0217979209053667.

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A Liouville integrable multi-component integrable system is obtained by the vector loop algebra. Then, the integrable couplings of the above system are presented by using the expanding vector loop algebra [Formula: see text] of the [Formula: see text]. Finally, the bi -Hamiltonian structure of the obtained system is given, respectively, by the variational identity.
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Bountis, Tassos, Zhanat Zhunussova, Karlygash Dosmagulova, and George Kanellopoulos. "Integrable and non-integrable Lotka-Volterra systems." Physics Letters A 402 (June 2021): 127360. http://dx.doi.org/10.1016/j.physleta.2021.127360.

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Olshanetsky, M. A. "Integrable extensions of classical elliptic integrable systems." Theoretical and Mathematical Physics 208, no. 2 (August 2021): 1061–74. http://dx.doi.org/10.1134/s0040577921080067.

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Výborný. "KURZWEIL-HENSTOCK ABSOLUTE INTEGRABLE MEANS McSHANE INTEGRABLE." Real Analysis Exchange 20, no. 1 (1994): 363. http://dx.doi.org/10.2307/44152498.

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Dissertations / Theses on the topic "Integrable"

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Meng, Jinghan. "Bi-Integrable and Tri-Integrable Couplings and Their Hamiltonian Structures." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4371.

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An investigation into structures of bi-integrable and tri-integrable couplings is undertaken. Our study is based on semi-direct sums of matrix Lie algebras. By introducing new classes of matrix loop Lie algebras, we form new Lax pairs and generate several new bi-integrable and tri-integrable couplings of soliton hierarchies through zero curvature equations. Moreover, we discuss properties of the resulting bi-integrable couplings, including infinitely many commuting symmetries and conserved densities. Their Hamiltonian structures are furnished by applying the variational identities associated with the presented matrix loop Lie algebras. The goal of this dissertation is to demonstrate the efficiency of our approach and discover rich structures of bi-integrable and tri-integrable couplings by manipulating matrix Lie algebras.
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Parini, Robert Charles. "Classical integrable field theories with defects and near-integrable boundaries." Thesis, University of York, 2018. http://etheses.whiterose.ac.uk/20428/.

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In the first part of this thesis algebro-geometric solutions for the sine-Gordon and KdV equations in the presence of a type I integrable defect are found, generalising the previously known soliton solutions. Elliptic (genus one) solutions where the defect induces only a phase shift are obtained via ansätze for the fields on each side of the defect. Algebro-geometric solutions for arbitrary genus and involving soliton emission by the defect are constructed using a Darboux transformation, exploiting the fact that the defect equations have the form of a Bäcklund transformation at a point. All the soliton and phase-shifted elliptic solutions to the defect equations are recovered as limits of the algebro-geometric solutions constructed in this way. Certain energy and momentum conserving defects for the Kadomtsev-Petviashvili equation are then presented as a first step towards the construction of integrable defects in higher dimensions. Algebro-geometric solutions to the sine-Gordon equation on the half-line with an integrable two parameter boundary condition are obtained by imposing a corresponding restriction on the Lax pair eigenfunction or, alternatively, as a Darboux transformation of the known algebro-geometric solution for the Dirichlet boundary. Finally, the collision of sine-Gordon solitons with a Robin type boundary is examined. This boundary is typically non-integrable but becomes an integrable Neumann or Dirichlet boundary for certain values of a boundary parameter. Depending on the boundary parameter and initial velocity an antikink may be reflected into various combinations of kinks, antikinks and breathers. The soliton content of the field after the collision is numerically determined by computing the discrete scattering data associated with the inverse scattering method. A highlight of this investigation is the discovery of an intricate structure of resonance windows caused by the production of a breather which can collide multiple times with the boundary before escaping as a lighter breather or antikink.
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Calini, Annalisa Maria. "Integrable curve dynamics." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186987.

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The Heisenberg Model of the integrable evolution of a continuous spin chain can be used to describe an integrable dynamics of curves in R ³. The role of orthonormal frames of the curve is explored. In this framework a second Poisson structure for the Heisenberg Model is derived and the relation between the Heisenberg Model and the cubic Non-Linear Schrodinger Equation is explained. The Frenet frame of a curve is shown to be a Legendrian curve in the space of orthonormal frames with respect to a natural contact structure. As a consequence, generic singularities of the solution of the Heisenberg Model and topological invariants of the curve are computed. The family of multi-phase solutions of the Heisenberg Model and the corresponding curves are constructed with techniques of algebraic geometry. The relation with the Non-Linear Schrodinger Equation is explained also in this context. A formula for the Backlund transformation for the Heisenberg Model is derived and applied to construct orbits homoclinic to planar circles. As a result singular knots are obtained.
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Saksida, Pavle. "Geometry of integrable systems." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308545.

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Cheng, Y. "Theory of integrable lattices." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.568779.

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This thesis deals with the theory of integrable lattices in "solitons" throughout. Chapter 1 is a general introduction, which includes an historical survey and a short surrunary of the "solitons" theory and the present work. In Chapter 2, we discuss the equivalence between two kinds of lattice AKNS spectral problems - one includes two potentials, while the other includes four. The two nonlinear lattice systems associated with those two spectral problems, respectively is also proved to be equivalent to each other. In Chapter 3, we derive a class of nonlinear differential-difference equations (NDDEs) and put them into the Hamiltonian systems. Their complete integrability are proved in terms of so called "r-matrix". In the end of this Chapter, we study the symmetry properties and the related topics for lattice systems. In particular, we give detail for the Toda lattice systems. Chapter 4 is concerned with the Backlund transformations (BTs) and nonlinear superposition formulae (NSFs) for a class of NDDEs. A new method is presented to derive the generalized BTs and to prove that these BTs are precisely and really the auto-BTs. The three kinds of NSFs are derived by analysis of so called "elementary BTs". In Chapter 5, we investigate some relations between our lattices and the well-studied continuous systems. The continuum limits of our lattice systems and the discretizations of the continuous systems are discussed. The other study is about how we can consider a BT of continuous systems as a NDDE and then how a BT of such a NDDE can be reduced to the three kinds of NSFs of the continuous systems. The last Chapter is a study of integrable lattices under periodic boundary conditions. It provides a mathematical foundation for the study of integrable models in statistical mechanics. We are particularly interested in the lattice sine-Gordon and sinh-Gordon models. We not only prove the integrability of these models but also derive all kinds of classical phase shifts and some other physically interesting relations.
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Moorhouse, Thomas. "Methods for integrable systems." Thesis, Durham University, 1994. http://etheses.dur.ac.uk/5484/.

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This work concerns the study of certain methods for investigating integrable systems, and the application of these methods to specific problems and examples. After introducing the notion of integrability in chapters 1 and 2, we go on, in chapter 3, to develop a novel type of discrete integrable equation by considering ways of enforcing Leibniz's rule for finite difference operators. We look at several approaches to the problem, derive some solutions and study several examples. Chapter 4 describes a numerical implementation of a method for solving initial value problems for an integrable equation in 2+1 dimensions, exploiting the integrability of the equation. The introduction of twisters enables a powerful scheme to be developed. In chapter 5 Darboux transformations derived from the factorisation of a scattering problem are examined, and a general operator form considered. The topic of chapter 6 is the relationship between the Darboux transform for the sine-Gordon and related equations and certain ansatze established by twistor methods. Finally in chapter 7 a geometric setting for partial differential equations is introduced and used to investigate the structure of Bäcklund transformations and generalised symmetries.
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Berntson, B. K. "Integrable delay-differential equations." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1566618/.

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Delay-differential equations are differential-difference equations in which the derivatives and shifts are taken with respect to the same variable. This thesis is concerned with these equations from the perspective of the theory of integrable systems, and more specifically, Painlevé equations. Both the classical Painlevé equations and their discrete analogues can be obtained as deautonomizations of equations solved by two-parameter families of elliptic functions. In analogy with this paradigm, we consider autonomous delay-differential equations solved by elliptic functions, delay-differential extensions of the Painlevé equations, and the interrelations between these classes of equations. We develop a method to identify delay-differential equations that admit families of elliptic solutions with at least two degrees of parametric freedom and apply it to two natural 16-parameter families of delay-differential equations. Some of the resulting equations are related to known models including the differential-difference sine-Gordon equation and the Volterra lattice; the corresponding new solutions to these and other equations are constructed in a number of examples. Other equations we have identified appear to be new. Bäcklund transformations for the classical Painlevé equations provide a source of delay-differential Painlevé equations. These transformations were previously used to derive discrete Painlevé equations. We use similar methods to identify delay-differential equations with continuum limits to the first classical Painlevé equation. The equations we identify are solved by elliptic functions in particular limits corresponding to the autonomous limit of the classical first Painlevé equation.
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Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.

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This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 Einstein equation the Belinski-Zakharov transformation is explored. It is used to derive explicit formula for N gravitational solitons on arbitrary diagonal background. In particular, the method is used to derive gravitational solitons on the Einstein-Rosen background. The similarities and differences between the attributes of the solitons of the symmetric Chiral field equation and those of the 1+1 Einstein equation are emphasized, and their origin is pointed out. For the 1+2 Einstein equation, new equations describing diagonal metrics are derived and their compatibility is proven. Different gravitational waves are studied that naturally extend the class of Bondi-Pirani-Robinson waves. It is further shown that the Bondi-Pirani-Robinson waves are stable with respect to perturbations of the spacetime. Their stability is closely related to the stability of the Schwarzschild black hole and the relation between the two allows to conjecture about the stability of a wide range of gravitational phenomena. Lastly, a new set of equations that describe weak gravitational waves is derived. This new system of equations is closely and fundamentally connected with the nonlinear Schrödinger equation and can be properly called the nonlinear Schrödinger-Einstein equations. A few preliminary solutions are constructed.
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McAnally, Morgan Ashley. "Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7423.

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We present a new spectral problem, a generalization of the D-Kaup-Newell spectral problem, associated with the Lie algebra sl(2,R). Zero curvature equations furnish the soliton hierarchy. The trace identity produces the Hamiltonian structure for the hierarchy. Lastly, a reduction of the spectral problem is shown to have a different soliton hierarchy with a bi-Hamiltonian structure. The first major motivation of this dissertation is to present spectral problems that generate two soliton hierarchies with infinitely many commuting conservation laws and high-order symmetries, i.e., they are Liouville integrable. We use the soliton hierarchies and a non-seimisimple matrix loop Lie algebra in order to construct integrable couplings. An enlarged spectral problem is presented starting from a generalization of the D-Kaup-Newell spectral problem. Then the enlarged zero curvature equations are solved from a series of Lax pairs producing the desired integrable couplings. A reduction is made of the original enlarged spectral problem generating a second integrable coupling system. Next, we discuss how to compute bilinear forms that are symmetric, ad-invariant, and non-degenerate on the given non-semisimple matrix Lie algebra to employ the variational identity. The variational identity is applied to the original integrable couplings of a generalized D-Kaup-Newell soliton hierarchy to furnish its Hamiltonian structures. Then we apply the variational identity to the reduced integrable couplings. The reduced coupling system has a bi-Hamiltonian structure. Both integrable coupling systems retain the properties of infinitely many commuting high-order symmetries and conserved densities of their original subsystems and, again, are Liouville integrable. In order to find solutions to a generalized D-Kaup-Newell integrable coupling system, a theory of Darboux transformations on integrable couplings is formulated. The theory pertains to a spectral problem where the spectral matrix is a polynomial in lambda of any order. An application to a generalized D-Kaup-Newell integrable couplings system is worked out, along with an explicit formula for the associated Bäcklund transformation. Precise one-soliton-like solutions are given for the m-th order generalized D-Kaup-Newell integrable coupling system.
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Jetzer, Frédéric. "Completely integrable systems on supermanifolds." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/NQ55399.pdf.

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Books on the topic "Integrable"

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Integrable models. Singapore: World Scientific, 1989.

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Babelon, Olivier, Yvette Kosmann-Schwarzbach, and Pierre Cartier, eds. Integrable Systems. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0315-5.

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Xing-Chang, Song, ed. Integrable systems. Singapore: World Scientific, 1990.

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Duistermaat, J. J. Discrete Integrable Systems. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-72923-7.

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Gerdjikov, V. S., G. Vilasi, and A. B. Yanovski, eds. Integrable Hamiltonian Hierarchies. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-77054-1.

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Konopelchenko, B. G., ed. Nonlinear Integrable Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-17567-9.

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Grammaticos, Basil, Thamizharasi Tamizhmani, and Yvette Kosmann-Schwarzbach, eds. Discrete Integrable Systems. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/b94662.

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Anindya, Ghose Choudhury, ed. Quantum integrable systems. Boca Raton: Chapman & Hall/CRC, 2003.

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1946-, Grammaticos B., Kosmann-Schwarzbach Yvette 1941-, and Tamizhmani T, eds. Discrete integrable systems. Berlin: Springer, 2004.

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D. J. J. F. Farnell. Integrable and non-integrablequantumarrays. Manchester: UMIST, 1994.

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Book chapters on the topic "Integrable"

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Santini, P. M. "Integrable Singular Integral Evolution Equations." In Springer Series in Nonlinear Dynamics, 147–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58045-1_9.

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Rodin, Yu L. "Integrable Systems." In Mathematics and Its Applications, 151–78. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2885-5_6.

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Brokate, Martin, and Götz Kersting. "Integrable Functions." In Compact Textbooks in Mathematics, 41–52. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15365-0_5.

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Shivamoggi, Bhimsen K. "Integrable Systems." In Fluid Mechanics and Its Applications, 127–95. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-2442-5_5.

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Tondeur, Philippe. "Integrable Forms." In Universitext, 8–23. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4613-8780-0_2.

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Arutyunov, Gleb. "Integrable Thermodynamics." In Elements of Classical and Quantum Integrable Systems, 335–69. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24198-8_6.

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Dubrovin, B. A., I. M. Krichever, and S. P. Novikov. "Integrable Systems.I." In Dynamical Systems IV, 177–332. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-06791-8_3.

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Gignoux, Claude, and Bernard Silvestre-Brac. "Integrable Systems." In Solved Problems in Lagrangian and Hamiltonian Mechanics, 281–339. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2393-3_6.

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Betounes, David. "Integrable Systems." In Differential Equations: Theory and Applications, 323–60. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-4971-7_8.

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Lam, Lui. "Integrable Systems." In Introduction to Nonlinear Physics, 213–33. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-2238-5_10.

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Conference papers on the topic "Integrable"

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KOREPIN, VLADIMIR I. "INTEGRABLE INTEGRAL OPERATORS." In Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812811264_0020.

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DEGASPERIS, A., D. D. HOLM, and A. N. W. HONE. "INTEGRABLE AND NON-INTEGRABLE EQUATIONS WITH PEAKONS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0005.

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DI FRANCESCO, PHILIPPE. "INTEGRABLE COMBINATORICS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0151.

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"Integrable Systems." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_others12.

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Xing-Chang, Song. "INTEGRABLE SYSTEMS." In Nankai Lectures on Mathematical Physics 1987. WORLD SCIENTIFIC, 1989. http://dx.doi.org/10.1142/9789814541381.

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ZHANG, YUFENG, and QINGYOU YAN. "A NEW INTEGRABLE HIERARCHY AND ITS EXPANSIVE INTEGRABLE MODEL." In Proceedings of the ICM2002 Satellite Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812795366_0016.

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Pyatov, P. N., and S. N. Solodukhin. "Geometry and Integrable Models." In Workshop of Geometry and Integrable Models. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814532556.

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PAVLOV, MAXIM V. "INTEGRABLE HYDRODYNAMIC CHAINS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0015.

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GAETA, GIUSEPPE, and PAOLA MORANDO. "QUATERNIONIC INTEGRABLE SYSTEMS." In Proceedings of the International Conference on SPT 2002. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812795403_0009.

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PREVIATO, EMMA. "SOME INTEGRABLE BILLIARDS." In Proceedings of the International Conference on SPT 2002. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812795403_0020.

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Reports on the topic "Integrable"

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Overman, Edward A., McLaughlin II, and David W. Whiskered Tori for Integrable Pde's: Chaotic Behavior in Near Integrable Pde's. Fort Belvoir, VA: Defense Technical Information Center, November 1994. http://dx.doi.org/10.21236/ada278390.

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Danilov, Viatcheslav, and Sergei Nagaitsev. On Quantum Integrable Systems. Office of Scientific and Technical Information (OSTI), November 2011. http://dx.doi.org/10.2172/1036292.

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Calini, Annalisa. Integrable Dynamics of Knotted Vortex Filaments. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-11-50.

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4

Batalov, I., and A. Valishev. Stability of non-linear integrable accelerator. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1038933.

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Stephan I. Tzenov. Renormalization Group Reduction of Non Integrable Hamiltonian Systems. Office of Scientific and Technical Information (OSTI), May 2002. http://dx.doi.org/10.2172/798173.

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Mohammedi, Nourddine. Classically Integrable Two-Dimensional Non-Linear Sigma Models. GIQ, 2015. http://dx.doi.org/10.7546/giq-16-2015-250-255.

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Moro, Antonio. High Frequency Integrable Regimes in Nonlocal Nonlinear Optics. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-7-2006-37-83.

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Bernatska, Julia, and Petro Holod. • Harmonic Analysis on Lagrangian Manifolds of Integrable Hamiltonian Systems. GIQ, 2012. http://dx.doi.org/10.7546/giq-14-2013-61-73.

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Bernatska and Petro Holod, Julia Bernatska and Petro Holod. Harmonic Analysis on Lagrangian Manifolds of Integrable Hamiltonian Systems. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-29-2013-39-51.

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Clem, P. G., D. Dimos, T. J. Garino, S. J. Martin, M. A. Mitchell, W. R. Olson, J. A. Ruffner, W. K. Schubert, and B. A. Tuttle. Surface Micromachined Flexural Plate Wave Device Integrable on Silicon. Office of Scientific and Technical Information (OSTI), January 1999. http://dx.doi.org/10.2172/2625.

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