On numerical solutions of a new coupled MKdV system by using the Adomian decomposition method and He's variational iteration method

Abstract

In this paper, we obtain the approximate solution for the soliton solution of a new coupled modified Korteweg-de Vries (MKdV) system with initial conditions by the Adomian decomposition method (ADM) and the variational iteration method (VIM) and then numerical results from the two methods are compared, showing that the ADM leads to more accurate results. Furthermore, the VIM overcomes the difficulty arising when calculating the Adomian polynomials, which is an important advantage over the ADM. The numerical results show that only a few terms are sufficient to obtain accurate solutions.