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Homoclinic breather-wave and singular periodic wave for a (2 + 1)D GSWW equation

Kang Xiaorong (School of Science, Southwest University of Science and Technology, Mianyang, China)
Xian Daquan (School of Science, Southwest University of Science and Technology, Mianyang, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 4 December 2018

Issue publication date: 22 February 2019

95

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

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