Exact solution of nonlinear Klein-Gordon equations with quadratic nonlinearity by modified Adomian decomposition method

Abstract

In this paper, we used the modified Adomian decomposition method (ADM) to obtain exact solution to Nonlinear Klein-Gordon equation (NK-GE) with quadratic nonlinearity. The paper contains an introduction and the concept of modified ADM for a generalized three-dimensional NK-GE. And, we applied this concept to obtain exact solution to two one-dimensional NK-GE with quadratic nonlinearity. The modified method is based on Taylors series expansion of the source term and implementation on any computer algebra software (Maple, Mathematica, etc) is simple. We discovered that the results of the examples considered are the same as the series solution of those obtained by using any known analytical method. Furthemore, we depicted our findings in three-dimensional surface and contour plots.