Application of Heʹs variational iteration method to nonlinear Jaulent–Miodek equations and comparing it with ADM

Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called Heʹs variational iteration method (VIM) is introduced to be applied to solve nonlinear Jaulent–Miodek, coupled KdV and coupled MKdV equations in this article. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with exact solutions.