Classical and nonclassical symmetries for a Kuramoto-Sivashinsky equation with dispersive effects

Abstract

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Kuramoto-Sivashinsky equation with dispersive effects. We make a full analysis of the symmetry reductions and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Some new solutions can be derived. Copyright © 2007 John Wiley & Sons, Ltd.