Extended symmetry analysis of generalized Burgers equations

TL;DR

This paper performs a comprehensive symmetry analysis of generalized Burgers equations, identifying their symmetries, reductions, and conservation laws to deepen understanding of their mathematical structure.

Contribution

It provides an extended classification of symmetries and transformations for generalized Burgers equations, improving upon previous results with a systematic approach.

Findings

Complete description of admissible transformations

Identification of Lie and nonclassical symmetries

Derivation of conservation laws

Abstract

Using advanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form $u_t+uu_x+f(t,x)u_{xx}=0$. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, conservation laws, potential admissible transformations and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.