A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations

By means of variational iteration method the solution of the Korteweg-de Vries Burgers (for short, KdVB) and a Lax’s seventh-order KdV (for short, LsKdV) equations are exactly obtained and in compared with that found by means of Adomian decomposition method. The comparison demonstrate that the two obtained solutions are an excellent agreement. The numerical results calculated and show that this method, variational iteration method, can be readily implemented to this type of nonlinear equations and excellent accuracy can be also achieved. The results of variation iteration method confirm the correctness of those obtained by mean of Adomian decomposition method.