Computational wave solutions of some nonlinear evolution equations

Abstract

This paper aims to realize some of the vital nonlinear evolution of partial differential equations in mathematical physics. We implement an extended simple equation (ESE) method to get exact and solitary traveling wave solutions of the Calogero-Degasperis (CD) equation, potential Kadomtsev–Petviashvili (pKP) equation, generalized Korteweg–de Vries (gKdV) equation, and the (2 + 1)–dimensional Zoomeron (Z) equation. We obtain a new form of solutions for each model as mentioned above. This method is considered a new, robust, practical, and direct method. As we see, the remarkable ability of this method to apply on the fractional and integer order of nonlinear partial differential equations.