Equivalence groupoid of generalized potential Burgers equations

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.