Novel localized waves and dynamics analysis for a generalized (3+1)-dimensional breaking soliton equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 30 August 2024
Issue publication date: 25 September 2024
Abstract
Purpose
This paper aims to explore new variable separation solutions for a new generalized (3 + 1)-dimensional breaking soliton equation, construct novel nonlinear excitations and discuss their dynamical behaviors that may exist in many realms such as fluid dynamics, optics and telecommunication.
Design/methodology/approach
By means of the multilinear variable separation approach, variable separation solutions for the new generalized (3 + 1)-dimensional breaking soliton equation are derived with arbitrary low dimensional functions with respect to {y, z, t}. The asymptotic analysis is presented to represent generally the evolutions of rogue waves.
Findings
Fixing several types of explicit expressions of the arbitrary function in the potential field U, various novel nonlinear wave excitations are fabricated, such as hybrid waves of kinks and line solitons with different structures and other interesting characteristics, as well as interacting waves between rogue waves, kinks, line solitons with translation and rotation.
Research limitations/implications
The paper presents that a variable separation solution with an arbitrary function of three independent variables has great potential to describe localized waves.
Practical implications
The roles of parameters in the chosen functions are ascertained in this study, according to which, one can understand the amplitude, shape, background and other characteristics of the localized waves.
Social implications
The work provides novel localized waves that might be used to explain some nonlinear phenomena in fluids, plasma, optics and so on.
Originality/value
The study proposes a new generalized (3 + 1)-dimensional breaking soliton equation and derives its nonlinear variable separation solutions. It is demonstrated that a variable separation solution with an arbitrary function of three independent variables provides a treasure-house of nonlinear waves.
Keywords
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 12275085 and No. 12235007) and the Science and Technology Commission of Shanghai Municipality (No. 21JC1402500 and No. 22DZ2229014).
Credit authorship contribution statement: Methodology, Software, Writing – original draft, Writing – review and editing. Methodology, Supervision, Writing – original draft, Writing – review and editing.
Declaration of competing interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability: No data was used for the research described in the article.
Citation
Quan, J. and Tang, X. (2024), "Novel localized waves and dynamics analysis for a generalized (3+1)-dimensional breaking soliton equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 10, pp. 3904-3923. https://doi.org/10.1108/HFF-04-2024-0298
Publisher
:Emerald Publishing Limited
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