Author:
Kumar Sachin,Gupta Rajesh Kumar,Kumari Pinki
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.
Subject
Applied Mathematics,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Cited by
3 articles.
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