Exact Solutions to New Potential Nonlinear Partial Differential Equations Using Extended Generalized Riccati Equation Mapping Method

Abstract

In this paper, we present a new model of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation, namely, potential of (KP-BBM), and potential of  the combined "Korteweg-de Vries and negative-order Korteweg-de Vries" with "Calogero-Bogoyavlenskii Schiff and negative-order Calogero-Bogoyavlenskii Schiff equation", namely, potential c(KdV-nKdV with CBS-nCBS). We apply the extended generalized Riccati equation mapping method to solve the new models. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions and  rational functions.