On some modified variational iteration methods for solving the one-dimensional sine-Gordon equation

In this paper, we present modified variational iteration methods (MVIM) to solve the sine-Gordon equation which play a very important part in applied and engineering sciences. Two versions of MVIM are made by the classical variational iteration method coupled with other methods such as homotopy perturbation method and Adomian decomposition method (ADM). The reliability and efficiency of the proposed methods are discussed and illustrated by numerical examples. Moreover, it has the advantage of higher precision and is easier to implement when compared with the ADM.