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Abstract: In this work, we applied Bäcklund transformation and similarity reduction for coupled Burger’s equation. Clarkson and Kruskal developed a direct and simple method to obtain more similarity solutions of nonlinear partial differential equation. We received our inspiration from Fan’s article, as far as we think that our work is an extended one from the Fan’s has done in his paper. As a result of this study, we obtained solitary wave solutions and traveling wave solutions of coupled Burger’s equation. [Copyright &y& Elsevier]

Abstract: In this paper, we found some exact solutions of the Cahn–Hilliard equation and the system of the equations by considering a modified extended tanh function method. A numerical solution to a Cahn–Hilliard equation is obtained using a homotopy perturbation method (HPM) combined with the Adomian decomposition method (ADM). The comparisons are given in the tables. [Copyright &y& Elsevier]

Abstract: In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker''s parabolic equation, the modified Korteweg–de Vries (KdV) equation, and the Sharma–Tasso–Olver (STO) equation with its fission and fusion, the Jaulent–Miodek equation. [Copyright &y& Elsevier]

Abstract: In this study, a decomposition method for approximating the solution of the generalized modified Boussinesq equation is implemented. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the decomposition series. The obtained results are found to be in good agreement with the exact solution. [Copyright &y& Elsevier]

In this paper an algorithm based on Adomian''s decomposition method is developed to approximate the solution of systems of nonlinear algebraic equations F(X)=0. Special cases of the system of nonlinear equations are solved using the algorithm of the decomposition method. It turns out that the convergence of this algorithm is rapid. The decomposition method has the advantage of being more concise for numerical purposes. [Copyright &y& Elsevier]