A Study on Degasperis-Procesi Equation By Iterative Methods

The degasperis-procesi equation can be derived as a member of a oneparameter family of asymptoticshallow water approximations to the euler equations with the same asymptotic accuracy as that ofthe camassa- holm equation. in this paper, the degasperis-procesi equation is solved by using theadomian's decomposition method , modied adomian's decomposition method , variational iterationmethod , modied variational iteration method, homotopy perturbation method, modied homotopyperturbation method and homotopy analysis method. the existence and uniqueness of the solutionand convergence of the proposed methods are proved in details. finally an example shows the accuracyof these methods.