On contact symmetries of evolution equations

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 $n\le 4$, and algebras having nontrivial Levi factors, belonging to the class under consideration, and corresponding contact symmetries they admitted are listed.

33 pages