An extended Painlevé integrable Kadomtsev--Petviashvili equation with lumps and multiple soliton solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 28 March 2023
Issue publication date: 19 May 2023
Abstract
Purpose
This study aims to propose an extended (3 + 1)-dimensional integrable Kadomtsev–Petviashvili equation characterized by adding three new linear terms.
Design/methodology/approach
This study formally uses Painlevé test to confirm the integrability of the new system.
Findings
The Painlevé analysis shows that the compatibility condition for integrability does not die away by adding three new linear terms with distinct coefficients.
Research limitations/implications
This study uses the Hirota's bilinear method to explore multiple soliton solutions where phase shifts and phase variable are explored.
Practical implications
This study also furnishes a class of lump solutions (LSs), which are rationally localized in all directions in space, using distinct values of the parameters via using the positive quadratic function method.
Social implications
This study also shows the power of the simplified Hirota’s method in handling integrable equations.
Originality/value
This paper introduces an original work with newly developed Painlevé integrable model and shows new useful findings.
Keywords
Acknowledgements
The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2023R17), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Compliance with ethical standards.
Conflict of interest: The authors declare no conflict of interest.
Data availability: Data sharing does not apply to this article, as no data sets were generated or analyzed during this study.
Citation
Wazwaz, A.-M., Alyousef, H.A. and El-Tantawy, S. (2023), "An extended Painlevé integrable Kadomtsev--Petviashvili equation with lumps and multiple soliton solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 7, pp. 2533-2543. https://doi.org/10.1108/HFF-01-2023-0039
Publisher
:Emerald Publishing Limited
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