New periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation

Many important physical situations such as fluid flows, plasma physics and solid-state physics have been described by (3+1)-dimensional generalized shallow water equation. In this article, we construct new periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation...

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Bibliographic Details
Published inNonlinear dynamics Vol. 90; no. 1; pp. 363 - 369
Main Authors Liu, Jian-Guo, He, Yan
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2017
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Nonlinear differential equations
Nonlinear equations
Original Paper
Plasma physics
Shallow water equations
Solid state physics
Solitary waves
Transformations (mathematics)
Vibration
68M07
33F10
Auto-Bäcklund transformation
Periodic solitary wave solutions
Symbolic computation
Generalized shallow water equation
35C08
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Summary:Many important physical situations such as fluid flows, plasma physics and solid-state physics have been described by (3+1)-dimensional generalized shallow water equation. In this article, we construct new periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation by using the auto-Bäcklund transformation and a direct test function. These obtained new periodic solitary wave solutions enrich the solution structure. Evidently, with the help of symbolic computation, the physical structure for these periodic solitary wave solutions is presented with some figures. The direct test function approach can be also applied to solve other nonlinear differential equations.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3667-y