Publication: Painleve Analysis and Symmetries of the HirotaSatsuma Equation
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Springer Science and Business Media LLC
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In this paper the authors show that the Painlevé analysis is a powerful tool for construction of symmetries, explicit solutions and Lie-Bäcklund transformations. It also helps to find Lax pairs and recursion operators and plays an important role in the study of a chaotic behaviour of nonlinear partial differential equations.
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Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, Hirota-Satsuma equation, analytical solution, KdV equations (Korteweg-de Vries equations), NLS equations (nonlinear Schrödinger equations), Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Geometric theory, characteristics, transformations in context of PDEs