On group classification of evolution equations admitting non-local symmetries

TL;DR

This paper develops a group classification method for evolution equations with non-local symmetries, showing that potential symmetries can be transformed into contact symmetries, and provides examples for second-order equations.

Contribution

It introduces a novel approach to classify evolution equations with non-local symmetries by reducing potential symmetries to contact symmetries, with practical examples.

Findings

Potential symmetries can be mapped to contact symmetries via reduction.

The group classification approach is effective for second-order evolution equations.

Several explicit classifications of equations with potential symmetries are provided.

Abstract

We prove that any evolution equation admitting a potential symmetry can always be reduced to another evolution equation such that the potential symmetry in question maps into the group of its contact symmetries. Based on this fact is out group approach to classification of evolution equations possessing non-local symmetries. We present several examples of classifications of second-order evolution equations admitting potential symmetries.