Study of a combined Kairat-II-X equation: Painlevé integrability, multiple kink, lump and other physical solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 6 August 2024
Issue publication date: 25 September 2024
Abstract
Purpose
This study aims to explore a novel model that integrates the Kairat-II equation and Kairat-X equation (K-XE), denoted as the Kairat-II-X (K-II-X) equation. This model demonstrates the connections between the differential geometry of curves and the concept of equivalence.
Design/methodology/approach
The Painlevé analysis shows that the combined K-II-X equation retains the complete Painlevé integrability.
Findings
This study explores multiple soliton (solutions in the form of kink solutions with entirely new dispersion relations and phase shifts.
Research limitations/implications
Hirota’s bilinear technique is used to provide these novel solutions.
Practical implications
This study also provides a diverse range of solutions for the K-II-X equation, including kink, periodic and singular solutions.
Social implications
This study provides formal procedures for analyzing recently developed systems that investigate optical communications, plasma physics, oceans and seas, fluid mechanics and the differential geometry of curves, among other topics.
Originality/value
The study introduces a novel Painlevé integrable model that has been constructed and delivers valuable discoveries.
Keywords
Acknowledgements
The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R229), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Compliance with ethical standards.
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.
Use of artificial intelligence (AI) tools declaration: The authors declare they have not used AI tools in the creation of this article.
Citation
Wazwaz, A.-M., Alhejaili, W. and El-Tantawy, S. (2024), "Study of a combined Kairat-II-X equation: Painlevé integrability, multiple kink, lump and other physical solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 10, pp. 3715-3730. https://doi.org/10.1108/HFF-05-2024-0411
Publisher
:Emerald Publishing Limited
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