New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 9 August 2021
Issue publication date: 19 April 2022
Abstract
Purpose
This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation.
Design/methodology/approach
This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.
Findings
This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense.
Research limitations/implications
This paper addresses the integrability features of this model via using the Painlevé analysis.
Practical implications
This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters.
Social implications
This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions.
Originality/value
To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.
Keywords
Acknowledgements
Compliance with ethical standards.
Conflict of interest: The author declares that he has no conflict of interest.
Citation
Wazwaz, A.-M. (2022), "New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 5, pp. 1664-1673. https://doi.org/10.1108/HFF-05-2021-0318
Publisher
:Emerald Publishing Limited
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