Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation

Abstract

Nonlinear partial differential equations are used to describe complex phenomena in various fields of science. In this work, we consider a generalized fourth‐order nonlinear wave equation from the point of view of the theory of symmetry reductions in partial differential equations. We derive classical symmetries, and we obtain the reductions from the optimal system of subalgebras. We derive all the low‐order conservation laws, and we search for multipliers of the reduced ordinary differential equations that are invariant under a symmetry group to reduce directly the order of the equations.