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Homoclinic breather waves, rouge waves and multi-soliton waves for a (2+1)-dimensional Mel’nikov equation

Na Liu (Business School, Shandong University of Political Science and Law, Jinan, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 December 2020

Issue publication date: 3 May 2021

102

Abstract

Purpose

The purpose of this paper is to study the homoclinic breather waves, rogue waves and multi-soliton waves of the (2 + 1)-dimensional Mel’nikov equation, which describes an interaction of long waves with short wave packets.

Design/methodology/approach

The author applies the Hirota’s bilinear method, extended homoclinic test approach and parameter limit method to construct the homoclinic breather waves and rogue waves of the (2 + 1)-dimensional Mel’nikov equation. Moreover, multi-soliton waves are constructed by using the three-wave method.

Findings

The results imply that the (2 + 1)-dimensional Mel’nikov equation has breather waves, rogue waves and multi-soliton waves. Moreover, the dynamic properties of such solutions are displayed vividly by figures.

Research limitations/implications

This paper presents efficient methods to find breather waves, rogue waves and multi-soliton waves for nonlinear evolution equations.

Originality/value

The outcome suggests that the extreme behavior of the homoclinic breather waves yields the rogue waves. Moreover, the multi-soliton waves are constructed, including the new breather two-solitary and two-soliton solutions. Meanwhile, the dynamics of these solutions will greatly enrich the diversity of the dynamics of the (2 + 1)-dimensional Mel’nikov equation.

Keywords

Acknowledgements

This work is supported by Shandong Provincial Government Grants, the National Natural Science Foundation of China-Shandong Joint Fund (No. U1806203), Program for Young Innovative Research Team in Shandong University of Political Science and Law and the Project of Shandong Province Higher Educational Science and Technology Program (No. J18KA234), the Project of Shandong University of Political Science and Law Scientific Research Program (No. 2020Z04A).

Citation

Liu, N. (2021), "Homoclinic breather waves, rouge waves and multi-soliton waves for a (2+1)-dimensional Mel’nikov equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 5, pp. 1695-1709. https://doi.org/10.1108/HFF-07-2020-0444

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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