Equivalence groupoid and enhanced group classification of a class of generalized Kawahara equations

TL;DR

This paper investigates the transformation properties of generalized Kawahara equations with time-dependent coefficients, constructing their equivalence groupoid, and provides a complete group classification by dividing the class into normalized subclasses.

Contribution

It introduces a novel approach to classify generalized Kawahara equations by analyzing their equivalence groupoid and dividing the class into normalized subclasses for comprehensive analysis.

Findings

The class is not normalized but can be split into two normalized subclasses.

Complete group classification of the class was achieved.

Gaps in previous classifications were addressed and filled.

Abstract

Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove that this class is not normalized but can be presented as a union of two disjoint normalized subclasses. Using the obtained results and properly gauging the arbitrary elements of the class, we carry out its complete group classification, which covers gaps in the previous works on the subject.