Applications of an Improved (GʹG) -expansion Method to Nonlinear PDEs in Mathematical Physics

Abstract

In the present article, we construct the traveling wave solutions of the (2+1)‐dimensional typical breaking soliton equation, the generalized (2+1)‐dimensional Boussinesq equation and the (1+1)‐dimensional symmetric regularized long wave equation by using an improved (G′G) ‐expansion method, where G satisfies a second order linear ordinary differential equation. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.