In this paper, the modified Kudryashov method (the rational Exp-function method) with the aid of symbolic computation has been applied to obtain exact solutions of the (2+1)-dimensional modified Korteweg-de Vries equations (mKdV) and nonlinear Drinfeld-Sokolov system. New exact solitary wave solutions are obtained with comparison of other solutions obtained before in literature.

In this paper, we use two integral methods, the first integral method and the direct integral method to study a higher-order nonlinear Schrödinger equation (NLSE). The application of the first integral method yield trigonometric function solutions and solitary wave solutions. Using the direct integration lead to shock wave solution and Jacobi elliptic function solutions. The direct integral method is more concise and direct than the first integral method.

In this paper, the variable coefficient two-dimensional Burger equation is studied by two distinct methods.The Exp-function method with the aid of symbolic computation is used to derive soliton solutions of this equation. The ' G G -expansion method is used also to construct travelling wave solutions for the variable coefficient two-dimensional Burger equation with the aid of symbolic computation. The travelling wave solutions are expressed by the hyperbolic, the trigonometric functions and rational functions. The study highlights the significant features of the employed methods and its capability of handling exact solutions for the variable coefficient two-dimensional Burger equation without any restrictions on the form of the variable coefficient. The obtained solutions are considered new with the comparison of other solutions obtained before.

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.