In this article, the variational iteration method (VIM) is used to obtain approximate analytical solutions of the modified Camassa-Holm and Degasperis-Procesi equations. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results reveal that the VIM is very effective.

In this paper, He's variational iteration method (VIM) has been used to obtain solution nonlinear gas dynamics equation and Stefan equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem.