Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations

TL;DR

This paper analyzes the symmetries and transformations of variable-coefficient Burgers equations, introducing a novel classification approach that partitions the equations into subclasses and identifies their equivalence groups.

Contribution

It develops a new method combining class splitting and mappings to classify symmetries of variable-coefficient Burgers equations.

Findings

Partition into two subclasses via differential constraints

Identification of normalized subclasses and their equivalence groups

Complete group classification with respect to the equivalence groupoid

Abstract

We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by families of point transformations parameterized by arbitrary elements of the original classes. A nontrivial differential constraint on the arbitrary elements of the class of variable-coefficient Burgers equations leads to its partition into two subclasses, which are related to normalized classes via families of point transformations parameterized by subclasses' arbitrary elements. One of the mapped classes is proved to be normalized in the extended generalized sense, and its effective extended generalized equivalence group is found. Using the mappings between classes and the algebraic method of group classification, we carry out the group classification of the initial class with respect to its equivalence groupoid.