A new Painlevé integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 May 2021
Issue publication date: 24 November 2021
Abstract
Purpose
This study aims to find the symmetries and conservation laws of a new Painlevé integrable Broer-Kaup (BK) system with variable coefficients. This system is an extension of dispersive long wave equations. As the system is generalized and new, it is essential to explore some of its possible aspects such as conservation laws, symmetries, Painleve integrability, etc.
Design/methodology/approach
This paper opted for an exploratory study of a new Painleve integrable BK system with variable coefficients. Some analytic solutions are obtained by Lie classical method. Then the conservation laws are derived by multiplier method.
Findings
This paper presents a complete set of point symmetries without any restrictions on choices of coefficients, which subsequently yield analytic solutions of the series and solitary waves. Next, the authors derive every admitted non-trivial conservation law that emerges from multipliers.
Research limitations/implications
The authors have found that the considered system is likely to be integrable. So some other aspects such as Lax pair integrability, solitonic behavior and Backlund transformation can be analyzed to check the complete integrability further.
Practical implications
The authors develop a time-dependent Painleve integrable long water wave system. The model represents more specific data than the constant system. The authors presented analytic solutions and conservation laws.
Originality/value
The new time-dependent Painleve integrable long water wave system features some interesting results on symmetries and conservation laws.
Keywords
Acknowledgements
The author, Pinki Kumari, conveys a sincere gratefulness to the University Grants Commission for assisting her financially in terms of senior research fellowship (SRF) via letter Ref. ID 19/06/2016(i)EU-V.
Citation
Kumar, S., Gupta, R.K. and Kumari, P. (2021), "A new Painlevé integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 12, pp. 3711-3721. https://doi.org/10.1108/HFF-02-2021-0094
Publisher
:Emerald Publishing Limited
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