Classification of classical and non-local symmetries of fourth-order nonlinear evolution equations

TL;DR

This paper classifies local and quasi-local symmetries of fourth-order nonlinear evolution equations, identifying both known and new equations with rich symmetry properties using Lie group analysis.

Contribution

It provides a comprehensive classification of symmetries for these equations, including new equations with complex symmetry structures, extending previous work on Lie group classifications.

Findings

Identified all inequivalent equations with semi-simple or solvable Lie symmetries.

Generated lists of invariant equations, including new ones with rich symmetry.

Extended classification to include quasi-local symmetries.

Abstract

In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent evolution equations belonging to the class under study which admit either semi-simple Lie groups or solvable Lie groups. The obtained lists of invariant equations (up to a local change of variables) contain both the well-known equations and a variety of new ones possessing rich symmetry. Based on the results on the group classification for local symmetries, the group classification for quasi-local symmetries of the equations is also given.