Exact Solutions of ϕ 4 Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

Abstract

This paper obtains the exact solutions of the ${\varphi }^4$ equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.