Kharrat-Toma Perturbation Method for Solving Linear and Nonlinear Klein- Gordon Equations

In this paper, we combine the Kharrat-Toma transform and the homotopy perturbation method for solving linear and nonlinear Klein-Gordon equations.Since the Klein-Gordon is two-variable equation, we first generalize the Kharrat-Toma transform to two-dimensional state.Then, we solve the linear Klein-Gordon equation only using the Kharrat-Toma transform and inverse Kharrat-Toma transform.Moreover, to solve the nonlinear Klein-Gordon equation, we combine the Kharrat-Toma transform with the homotopy perturbation method and obtain an approximate solution for it.Finally, we give some examples for both cases and compute the error of the approximate solutions.