Bäcklund transformation and CRE solvability for the negative-order modified KdV equation

DOI10.1007/S11071-017-3682-ZzbMath1390.37120OpenAlexW2738017913MaRDI QIDQ1749876

Junfeng Song, Zheng-Yi Ma, Ya-Hong Hu

Publication date: 17 May 2018

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-017-3682-z

zbMATH Keywords

\(n\)th Bäcklund transformationresidual symmetryexact interaction solutionconsistent Riccati expansion solvabilitynegative-order modified KdV equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (9)

Residual symmetries, \(n\)th Bäcklund transformation and interaction solutions for (2+1)-dimensional generalized Broer-Kaup equations ⋮ Residual symmetry, Bäcklund transformation and CRE solvability of a \((2+1)\)-dimensional nonlinear system ⋮ \(N\)-th Bäcklund transformation and soliton-cnoidal wave interaction solution to the combined KdV-negative-order KdV equation ⋮ Nonlocal residual symmetries and exact interaction solutions for the generalized dispersive water waves system ⋮ Nonlocal symmetry and similarity reductions for a \((2+1)\)-dimensional Korteweg-de Vries equation ⋮ New Bäcklund transformations of the \((2+1)\)-dimensional Bogoyavlenskii equation via localization of residual symmetries ⋮ Residual Symmetry of the Alice-Bob Modified Korteweg-de Vries Equation* ⋮ Bäcklund transformation, residual symmetry and exact interaction solutions of an extended \((2+1)\)-dimensional Korteweg-de Vries equation ⋮ Consistent Riccati expansion solvability and soliton-cnoidal wave solutions of a coupled KdV system

Cites Work

• Residual symmetries and interaction solutions for the Whitham-Broer-Kaup equation
• Nonlocal symmetry, CRE solvability and soliton-cnoidal solutions of the \((2+1)\)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation
• CTE method to the interaction solutions of Boussinesq-Burgers equations
• The \((2+1)\)-dimensional Konopelchenko-Dubrovsky equation: nonlocal symmetries and interaction solutions
• Negative-order modified KdV equations: multiple soliton and multiple singular soliton solutions
• Negative powers of Olver recursion operators
• The Painlevé property for partial differential equations
• Evolution equations possessing infinitely many symmetries
• Consistent Riccati Expansion for Integrable Systems

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