Two Integral Methods Applied to the (2+1) Dimensional Davey-Stewartson Equation

In this paper, we use two integral methods, the first integral method and the direct integral method to study (2+1)- dimensional Davey-Stewartson equation . The first integral method was used to construct travelling wave solutions, those solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. By using the direct integration method shock wave solution and Jacobi elliptic function solutions are obtained. By comparison between the two methods, the direct integration is more impressive than the first integral method. The results obtained confirm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear systems of partial differential equations.