Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations

TL;DR

This paper classifies the transformations of a class of variable coefficient Korteweg--de Vries equations, revealing their structure and partitioning into subclasses, and performs group classification for one subclass.

Contribution

It provides a comprehensive classification of admissible transformations and the structure of the equivalence groupoid for these equations, including subclass partitioning and group classification.

Findings

The class is partitioned into six normalized subclasses.

The widest possible equivalence groups are identified for each subclass.

Group classification is completed for one representative subclass.

Abstract

We classify the admissible transformations in a class of variable coefficient Korteweg--de Vries equations. As a result, full description of the structure of the equivalence groupoid of the class is given. The class under study is partitioned into six disjoint normalized subclasses. The widest possible equivalence group for each subclass is found which appears to be generalized extended in five cases. Ways for improvement of transformational properties of the subclasses are proposed using gaugings of arbitrary elements and mapping between classes. The group classification of one of the subclasses is carried out as an illustrative example.