Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto–Sivashinsky Equation

Abstract

Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto–Sivashinsky (KS) equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.