Group classification of the general evolution equation: local and quasi-local symmetries

TL;DR

This paper extends the classification of evolution equations to include local and quasi-local symmetries, revealing new classes with nontrivial Lie symmetries and quasilocal symmetries.

Contribution

It generalizes previous classifications to broader evolution equations, identifying new symmetry classes and quasilocal symmetries.

Findings

Several new classes of evolution equations with nontrivial Lie symmetries

Derivation of nonlinear evolution equations with quasilocal symmetries

Enhanced understanding of symmetry structures in evolution equations

Abstract

We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with nontrivial Lie symmetry. As a by-product, we derive a number of nonlinear evolution equations admitting quasilocal symmetries.