Simple equation method for nonlinear partial differential equations and its applications

In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs) such as, Kodomtsev–Petviashvili (KP) equation, the (2 + 1)-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.