A symmetry classification for a class of (2+1)-nonlinear wave equation

TL;DR

This paper performs a symmetry classification of a (2+1)-dimensional nonlinear wave equation using Lie group methods, identifying its symmetry groups based on the form of the function f(u).

Contribution

It provides a systematic Lie group analysis and classification for a class of (2+1)-nonlinear wave equations, which was not previously detailed.

Findings

Determined the general symmetry group of the equation.

Classified the equation based on different forms of f(u).

Presented a method for calculating symmetry groups of nonlinear PDEs.

Abstract

In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $(2+1)$-nonlinear wave equation.