Resonant Soliton and Soliton-Cnoidal Wave Solutions for a (3+1)-Dimensional Korteweg-de Vries-Like Equation

The residual symmetry of a (3+1)-dimensional Korteweg-de Vries (KdV)-like equation is constructed using the truncated Painlevé expansion. Such residual symmetry can be localized and the (3+1)-dimensional KdV-like equation is extended into an enlarged system by introducing some new variables. By usin...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2019, Vol.2019 (2019), p.1-11
Main Authors: Zhu, Quan-Yong, Chen, Jun-Chao, Fei, Jinxi, Ma, Zhengyi
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary value problems
Cnoidal waves
Jacobian elliptic functions
Korteweg-Devries equation
Lie groups
Partial differential equations
Physics
Solitary waves
Superposition (mathematics)
Symmetry
Transformations (mathematics)
Variables
Wave interaction
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Summary:The residual symmetry of a (3+1)-dimensional Korteweg-de Vries (KdV)-like equation is constructed using the truncated Painlevé expansion. Such residual symmetry can be localized and the (3+1)-dimensional KdV-like equation is extended into an enlarged system by introducing some new variables. By using Lie’s first theorem, the finite transformation is obtained for this localized residual symmetry. Further, the linear superposition of multiple residual symmetries is localized and the n-th Bäcklund transformation in the form of the determinants is constructed for this equation. For illustration more detail, the first three multiple wave solutions-the collisions of resonant solitons are depicted. Finally, with the aid of the link between the consistent tanh expansion (CTE) method and the truncated Painlevé expansion, the explicit soliton-cnoidal wave interaction solution containing three kinds of Jacobian elliptic functions for this equation is derived.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/8034731