A new Painlevé integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws. Issue 12 (7th May 2021)

• Record Type: Journal Article
• Authors: Kumar, Sachin; Gupta, Rajesh Kumar; Kumari, Pinki
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 31:Issue 12(2021)
• Page Start: 3711
• Page End: 3721
• Publication Date: 2021-05-07
• Subjects: Symmetry -- Exact solution -- Broer-Kaup system -- Conservation law -- Painleve integrability; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-02-2021-0094
• Languages: English
• ISSNs: 0961-5539

Abstract

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.