Nonlocal symmetries of systems of evolution equations

TL;DR

This paper demonstrates that potential symmetries of evolution equations can be transformed into Lie symmetries via nonlocal transformations, and introduces an algebraic method for classifying more general nonlocal symmetries with several examples.

Contribution

It provides a novel algebraic approach to classify nonlocal symmetries of evolution equations, extending previous methods by incorporating nonlocal transformations.

Findings

Potential symmetries reduce to Lie symmetries under nonlocal transformations

New algebraic method for classifying nonlocal symmetries

Several illustrative examples of the classification process

Abstract

We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of evolution equations having non-trivial Lie symmetry. Next, we modify the above method to generate more general nonlocal symmetries, which yields a purely algebraic approach to classifying nonlocal symmetries of evolution type systems. Several examples are considered.