The Sine-Cosine Functions Method for solving nonlinear partial differential equations

Abstract

The Sine-Cosine function algorithm is applied for solving nonlinear partial differential equations. Such as Traveling Wave Solutions, which are obtained by using a relatively new technique, which is called Sine-Cosine function Method for Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZK-BBM) equations. Solutions procedure and obtained results reconfirm the efficiency of the proposed scheme. In this thesis the Sine-Cosine function method has some analytic solutions for the generalized (2+1)-dimensional nonlinear evolution equation is presented (2+1)-dimensional Breaking soliton equation, (2+1)-dimensional Calogero - Bogoyavlenskii-Schiff (CBS) equation , (2+1)-dimensional Bogoyavlenskii's Breaking soliton equation is chosen to illustrate the effectiveness of the method,and we establish exact solutions for nonlinear Davey-Stewartson equations, and also used to construct periodic and solitary wave solutions. The Sine-Cosine function method is used to obtain the exact solutions for different type of nonlinear partial differential equations.