Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple soliton solutions and a class of lump solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 23 December 2022
Issue publication date: 25 April 2023
Abstract
Purpose
This paper aims to propose a new (3+1)-dimensional integrable Hirota bilinear equation characterized by five linear partial derivatives and three nonlinear partial derivatives.
Design/methodology/approach
The authors formally use 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
The Painlevé analysis shows that the compatibility condition for integrability does not die away at the highest resonance level, but integrability characteristics is justified through the Lax sense.
Research limitations/implications
Multiple-soliton solutions are explored using the Hirota's bilinear method. The authors also furnish a class of lump solutions using distinct values of the parameters via the positive quadratic function method.
Practical implications
The authors also retrieve a bunch of other solutions of distinct structures such as solitonic, periodic solutions and ratio of trigonometric functions solutions.
Social implications
This work formally furnishes algorithms for extending integrable equations and for the determination of lump solutions.
Originality/value
To the best of the authors’ knowledge, this paper introduces an original work with newly developed Lax-integrable equation and shows new useful findings.
Keywords
Acknowledgements
Conflict of interest: The author declares that he has no conflict of interest.
Data availability: Data sharing does not apply to this article as no data sets were generated or analyzed during the current study.
Citation
Wazwaz, A.-M., El-Sherif, L. and El-Tantawy, S. (2023), "Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple soliton solutions and a class of lump solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 5, pp. 1837-1852. https://doi.org/10.1108/HFF-09-2022-0543
Publisher
:Emerald Publishing Limited
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