Equivalence groupoid of generalized potential Burgers equations

TL;DR

This paper characterizes the complex structure of the equivalence groupoid for generalized potential Burgers equations, dividing the class into three normalized subclasses with specific transformation groups.

Contribution

It provides a detailed description of the equivalence groupoid for a class of second-order evolution equations, including the partition into normalized subclasses and their transformation groups.

Findings

The equivalence groupoid has a complex structure.

The class is partitioned into three normalized subclasses.

Each subclass has its own specific equivalence group.

Abstract

We find the equivalence groupoid of a~class of $(1+1)$-dimensional second-order evolution equations, which are called generalized potential Burgers equations. This class is related via potentialization with two classes of variable-coefficient generalized Burgers equations. Its equivalence groupoid is of complicated structure and is described via partitioning the entire class into three normalized subclasses such that there are no point transformations between equations from different subclasses. For each of these subclasses we construct its equivalence group of an appropriate kind.