Preliminary group classification for generalized inviscid Burger's equation

TL;DR

This paper performs a preliminary group classification of a broad class of generalized inviscid Burger's equations, identifying new invariant models and equivalence transformations to enhance understanding of their symmetry properties.

Contribution

It introduces a comprehensive classification of generalized inviscid Burger's equations, including new nonlinear invariant models and equivalence transformations, extending recent research.

Findings

Identification of new nonlinear invariant models

Derivation of additional equivalence transformations

Compilation of a wide class of equations in table form

Abstract

Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially generalize recent works on the subject . A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.