Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations

In this paper, by means of variational iteration method numerical and explicit solutions are computed for some fifthorder Korteweg-de Vries equations, without any linearization or weak nonlinearity assumptions. These equations are the Kawahara equation, Lax’s fifth-order KdV equation and Sawada–Kotera equation. Comparison with Adomian decomposition method reveals that the variational iteration method is easier to be implemented. We conclude that the method is a promising method to various kinds of fifth-order Korteweg-de Vries equations.

KdV-equation; exp-function method; Adomian decomposition method