On contact symmetries of evolution equations

TL;DR

This paper develops an algebraic framework to classify contact symmetries of second-order nonlinear evolution equations, identifying all inequivalent PDEs with specific symmetry algebra structures.

Contribution

It provides a comprehensive classification of contact symmetries for a class of evolution equations based on algebraic methods, including semi-simple and solvable algebras.

Findings

Classified PDEs with semi-simple symmetry algebras

Identified PDEs with solvable symmetry algebras of dimension ≤4

Listed PDEs with nontrivial Levi factors and their symmetries

Abstract

In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable algebras of dimension $n\leq4$, and algebras having nontrivial Levi factors, belonging to the class under consideration, and corresponding contact symmetries they admitted are listed.