Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalised variable coefficient shallow water wave equation

TL;DR

This paper derives nonlocal symmetries and exact solutions for a (2+1)-dimensional variable coefficient shallow water wave equation using Painleve analysis, Lie symmetries, and Schwartzian equations, revealing complex wave interactions.

Contribution

It introduces a method to localize nonlocal symmetries and constructs exact interaction solutions for the generalized SWW equation, advancing analytical techniques in nonlinear wave equations.

Findings

Derived Schwartzian equation via Painleve analysis

Constructed nonlocal symmetries using Lax pairs

Obtained exact soliton-cnoidal wave interaction solutions

Abstract

In this paper, using the standard truncated Painleve analysis, the Schwartzian equation of (2+1)-dimensional generalised variable coefficient shallow water wave (SWW)equation is obtained. With the help of lax pairs, nonlocal symmetries of the SWW equation are constructed which be localized by a complicated calculation process. Furthermore, using the Lie point symmetries of the closed system and Schwartzian equation, some exact interaction solutions are obtained, such as soliton-cnoidal wave solutions. Corresponding 2D and 3D figures are placed on illustrate dynamic behavior of the generalised variable coefficient SWW equation.