homotopy perturbation and elzaki transform for solving sine-gorden and klein-gorden equations

in this paper, the homotopy perturbation method (hpm) and elzaki transform is employed to obtain the approximate analytical solution of the sine gorden and the klein gorden equations. the nonlinear terms can be handled by the use of homotopy perturbation method. the proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads to the solution in terms of transformed variable, and the series solution that can be obtained by making use of the inverse transformation.