Equivalence groupoid of a class of general Burgers-Korteweg-de Vries equations with space-dependent coefficients

Abstract

We describe the equivalence groupoid of the class of general Burgers-Korteweg-de Vries equations with space-dependent coefficients.
This class is shown to reduce by a family of equivalence transformations to a subclass with a four-dimensional usual equivalence group.
Classified are admissible transformations of this subclass and singled out its subclasses admitting maximal nontrivial conditional equivalence groups.
All of them turn out to have dimension higher than four.
In particular, few new examples of nontrivial cases of normalization in the generalized sense of classes of differential equations
appeared this way. Neither of classes discussed possesses a unique effective generalized equivalence group.