Symmetry group classification for general Burger's equation

TL;DR

This paper classifies symmetries of a generalized Burgers' equation using Lie methods, identifying new invariant models and providing a comprehensive table of equations with their symmetry properties.

Contribution

It applies the algebraic method of preliminary group classification to a broad class of Burgers' equations, revealing new nonlinear invariant models.

Findings

Identification of equations with nontrivial invariance algebras

Development of a classification table for the equations

Application of algebraic approach to symmetry analysis

Abstract

The present paper solves the problem of the group classification of the general Burgers' equation $u_t=f(x,u)u_x^2+g(x,u)u_{xx}$, where $f$ and $g$ are arbitrary smooth functions of the variable $x$ and $u$, by using Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification: the method of preliminary group classification. A number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.