A modified homotopy perturbation method to periodic solution of a coupled integrable dispersionless equation

In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and Pade approximation, known as aftertreatment technique, is proposed. The angular frequencies are compared with the exact frequency. Comparison of the approximated results and exact one shows a good agreement.