Group classification of nonlinear evolution equations: Semi-simple groups of contact transformations

Abstract

We generalize and modify the group classification approach of Zhdanov and Lahno (1999) to make it applicable beyond Lie point symmetries. This approach enables obtaining exhaustive classification of second-order nonlinear evolution equations in one spatial dimension invariant under semi-simple groups of contact transformations. What is more, all inequivalent second-order nonlinear evolution equations which admit semi-simple groups or groups having nontrivial Levi decompositions are constructed in explicit forms.