Solutions of Two Nonlinear Evolution Equations Using Lie Symmetry and Simplest Equation Methods

Abstract

In this paper, we study two nonlinear evolution partial differential equations, namely, a modified Camassa-Holm-Degasperis-Procesi equation and the generalized Korteweg-de Vries equation with two power law nonlinearities. For the first time, the Lie symmetry method along with the simplest equation method is used to construct exact solutions for these two equations.