Novel Exact Solutions of the Extended Shallow Water Wave and the Fokas Equations

Abstract

In this study, a Sine-Gordon expansion method for obtaining novel exact solutions of extended shallow water wave equation and Fokas equation is presented. All of the equations which are under consideration consist of three or four variable. In this method, first of all, partial differential equations are reduced to ordinary differential equations by the help of variable change called as travelling wave transformation, then Sine Gordon expansion method allows us to obtain new exact solutions defined as in terms of hyperbolic trig functions of considered equations. The newly obtained results showed that the method is successful and applicable and can be extended to a wide class of nonlinear partial differential equations.