Lie symmetries and conservation laws for a generalized Kuramoto- Sivashinsky equation.

Abstract

Nonlinear partial differential equations are used to describe complex phe-nomena in various fields of science. In this work, we consider a generalizedfourth-order nonlinear wave equation from the point of view of the theory ofsymmetry reductions in partial differential equations. We derive classical sym-metries, and we obtain the reductions from the optimal system of subalgebras.We derive all the low-order conservation laws, and we search for multipliers ofthe reduced ordinary differential equations that are invariant under a symmetrygroup to reduce directly the order of the equatio