Residual symmetry, nth Bäcklund transformation, and soliton‐cnoidal wave interaction solution for the combined modified KdV–negative‐order modified KdV equation

DOI10.1002/mma.5935zbMath1446.35161OpenAlexW2990778486MaRDI QIDQ5116840

Deqin Qiu, Tian-Zhou Xu, Wen-guang Cheng

Publication date: 19 August 2020

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.5935

zbMATH Keywords

interaction solution\(n\)th Bäcklund transformationresidual symmetryconsistent Riccati expansioncombined modified KdV-negative-order modified KdV equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear waves in solid mechanics (74J30) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

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Shallow water in an open sea or a wide channel: auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system ⋮ Nonlocal residual symmetries and exact interaction solutions for the generalized dispersive water waves system ⋮ Consistent Riccati expansion solvability and soliton-cnoidal wave solutions of a coupled KdV system

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