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

Homoclinic breather waves, rouge waves and multi-soliton waves for a (2+1)-dimensional Mel’nikov... 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/approachThe 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.FindingsThe 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/implicationsThis paper presents efficient methods to find breather waves, rogue waves and multi-soliton waves for nonlinear evolution equations.Originality/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0961-5539
eISSN
0961-5539
DOI
10.1108/hff-07-2020-0444
Publisher site
See Article on Publisher Site

Abstract

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/approachThe 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.FindingsThe 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/implicationsThis paper presents efficient methods to find breather waves, rogue waves and multi-soliton waves for nonlinear evolution equations.Originality/valueThe 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.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: May 3, 2021

Keywords: Mel’nikov equation; Hirota bilinear form; Homoclinic breather wave; Rogue wave; Multi-soliton wave

References