Symplectic structures, their B?acklund transformation and hereditary symmetries

Keywords

Symplectic geometry, Homogeneous space, Mathematics, Symmetry (geometry), Operator (biology)

References

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• Les variétés de Poisson et leurs algèbres de Lie associéesAndré Lichnerowicz — 1977
• Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear MediaВ. Е. Захаров, A. B. Shabat — 1970
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• Fractional powers of operators and Hamiltonian systemsI. M. Gel'fand, L. A. Dikii — 1976
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• Application of hereditary symmetries to nonlinear evolution equationsBenno Fuchssteiner — 1979
• On the structure of symplectic operators and hereditary symmetriesA. S. Fokas, Benno Fuchssteiner — 1980
• Almost Periodic Solutions of the KdV EquationPeter D. Lax — 1976
• A Lie algebra structure in a formal variational calculationI. M. Gel'fand, L. A. Dikii — 1976
• Evolution equations possessing infinitely many symmetriesPeter J. Olver — 1977
• Pure soliton solutions of some nonlinear partial differential equationsBenno Fuchssteiner — 1977
• Bäcklund transformations for hereditary symmetriesA. S. Fokas, Benno Fuchssteiner — 1981
• INTEGRALS OF NONLINEAR EQUATIONS OF EVOLUTION AND SOLITARY WAVES.Peter D. Lax — 1968
• A Simple model of the integrable Hamiltonian equationFranco Magri — 1978
• Deformation theory and quantization. I. Deformations of symplectic structuresF. Bayen, M. Flato, C. Frønsdal — 1978
• On the Hamiltonian structure of evolution equationsPeter J. Olver — 1980
• Internal waves of permanent form in fluids of great depthT. Brooke Benjamin — 1967
• A new hierarchy of Korteweg–de Vries equationsP. J. Caudrey, R. K. Dodd, John Gibbon — 1976
• A symmetry approach to exactly solvable evolution equationsA. S. Fokas — 1980

Cited by

• Hamiltonian systems on fibered manifoldsYvette Kosmann–Schwarzbach — 1981
• Breakdown of a shallow water equationH. P. McKean — 1998
• To the Classif ication of Integrable Systems in 1+1 DimensionsI. V. Kulemin, A. G. Meshkov — 1997
• Some distributional solutions of the CH, DP and CH2 equations and the Lax pair formalismKeivan Mohajer — 2008
• On the blow-up phenomena of Cauchy problem for the Camassa-Holm equationYongqin Liu, Wang Weike — 2006
• On the isospectral problem of the Camassa-Holm equationJonathan Eckhardt — 2011
• The Study of Solution of Dissipative Camassa-Holm Equation on Total SpaceDanping Ding, Lixin Tian — 2006
• On a periodic 2-component μ-Hunter-Saxton equationJingjing Liu, Zhaoyang Yin — 2010
• The General Two Dimensional Shifted Jacobi Matrix Method for Solving the Second Order Linear Partial Difference-differential Equations with Variable CoefficientsZ. Kalateh Bojdi, Salman Ahmadi‐Asl, A. Aminataei — 2013
• Finite-Dimensional Reductions of Conservative Dynamical Systems and Numerical Analysis. IA. K. Prykarpats’kyi, Stanis law Brzychczy, В. Г. Самойленко — 2001
• On the Cauchy problem for a new integrable two-component system with peakon and weak kink solutionsKai Yan, Zhijun Qiao, Zhaoyang Yin — 2013
• Bi-Integrable and Tri-Integrable Couplings and Their Hamiltonian StructuresJinghan Meng — 2012
• Global Weak Solutions for the Weakly Dissipative Camassa-Holm EquationShuyin Wu — 2011
• The Structure of Cosymmetries and a Simple Proof of Locality for Hierarchies of Symmetries of Odd Order Evolution SystemsArtur Sergyeyev — 2004
• Non-local Poisson structures and applications to the theory of integrable systemsAlberto De Sole, Victor G. Kač — 2012
• Numerical superposition of Gaussian beams over propagating domain for high frequency waves and high-order invariant-preserving methods for dispersive wavesNattapol Ploymaklam — 2014
• On a shallow water wave equationXavier Raynaud — 2006
• Asymptotic Approximations of Gravity Waves in WaterArne Kristian Jansen — 2009
• The Peakon Limits of Soliton Solutions of the Camassa-Holm Equation(General)A. Parker, Yoshimasa Matsuno — 2006
• Geometric integration of nonlinear wave equationsMorten Dahlby — 2007

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