An explicit and numerical solutions of some fifth-order KdV equation by decomposition method

摘要

In this paper, by considering the Adomian decomposition method, explicit and numerical solutions are calculated for a various fifth-order Korteweg-de Vries equations with initial condition. The method does not need linearization or weak nonlinearity assumptions, perturbation theory. The decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self-canceling “noise” terms where sum of components vanishes in the limit.