Towards classification of quasi-local symmetries of evolution equations

TL;DR

This paper introduces a group-theoretical method for classifying evolution equations that admit quasi-local symmetries involving integrals of the dependent variable, extending to systems with two independent variables.

Contribution

It develops a systematic approach to classify evolution equations with quasi-local symmetries and generalizes it to systems with multiple equations and variables.

Findings

Classified realizations of two- and three-dimensional Lie algebras with quasi-local symmetries.

Extended the classification approach to arbitrary systems of evolution equations with two variables.

Abstract

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We classify realizations of two- and three-dimensional Lie algebras leading to equations admitting quasi-local symmetries. Finally, we generalize the approach in question for the case of an arbitrary system of evolution equations with two independent variables.