Integrability of linear structure of components of modified Korteweg–De Vries hierarchy: multiple soliton solutions and breathers solutions
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 June 2023
Issue publication date: 21 July 2023
Abstract
Purpose
The purpose of this study is to form a linear structure of components of the modified Korteweg–De Vries (mKdV) hierarchy. The new model includes 3rd order standard mKdV equation, 5th order and 7th order mKdV equations.
Design/methodology/approach
The authors investigate Painlevé integrability of the constructed linear structure.
Findings
The Painlevé analysis demonstrates that established sum of integrable models retains the integrability of each component.
Research limitations/implications
The research also presents a set of rational schemes of trigonometric and hyperbolic functions to derive breather solutions.
Practical implications
The authors also furnish a variety of solitonic solutions and complex solutions as well.
Social implications
The work formally furnishes algorithms for extending integrable equations that consist of components of a hierarchy.
Originality/value
The paper presents an original work for developing Painlevé integrable model via using components of a hierarchy.
Keywords
Acknowledgements
The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2023R229), 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.
Citation
Wazwaz, A.-M., Alhejaili, W. and El-Tantawy, S. (2023), "Integrability of linear structure of components of modified Korteweg–De Vries hierarchy: multiple soliton solutions and breathers solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 9, pp. 3111-3123. https://doi.org/10.1108/HFF-03-2023-0154
Publisher
:Emerald Publishing Limited
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