Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 4 December 2018
Issue publication date: 22 February 2019
Abstract
Purpose
The purpose of this paper is to discuss the homoclinic breathe-wave solutions and the singular periodic solutions for (2 + 1)-dimensional generalized shallow water wave (GSWW) equation.
Design/methodology/approach
The Hirota bilinear method, the Lie symmetry method and the non-Lie symmetry method are applied to the (2 + 1)D GSWW equation.
Findings
A reduced (1 + 1)D potential KdV equation can be derived, and its soliton solutions are also presented.
Research limitations/implications
As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.
Originality/value
These results are very useful for investigating some localized geometry structures of dynamical behaviors and enriching dynamical features of solutions for the higher dimensional systems.
Keywords
Acknowledgements
This work was supported by Longshan Scholar Talent Research Supporting Program of SWUST (17LZXY04, 17LZXJ05).
Citation
Xiaorong, K. and Daquan, X. (2019), "Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 3, pp. 1000-1009. https://doi.org/10.1108/HFF-08-2018-0436
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited