Symmetry Classification of Third-Order Nonlinear Evolution Equations. Part I: Semi-simple Algebras

Abstract

We give a complete point-symmetry classification of all third-order evolution equations of the form u t =F(t,x,u,u x ,u xx )u xxx +G(t,x,u,u x ,u xx ) which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.