Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations

In this paper, He's variational iteration method (VIM) is employed successfully for solving modified Camassa-Holm and Degasperis-Procesi equations. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or the perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving nonlinear differential equations with fully nonlinear dispersion term. It is predicted that VIM can be widely applied in science and engineering problems. Copyright (C) 2008 John Wiley & Sons, Ltd.