Solitary wave solutions for the general KDV equation by Adomian decomposition method

摘要

In recent publications [Chaos, Solitons Fractals 12 (2001) 2283; Int. J. Appl. Math. 3 (4) (2000) 361], we have dealt with the numerical solutions of the Korteweg–De-Vries (KDV) and modified Korteweg–De-Vries (MKDV) equations. We extend this study to a more general nonlinear equation, which is the general Korteweg–De-Vries (GKDV) equation, in which the previous studies is a special case of it. The method applied here is Adomian decomposition method, which has been developed by George Adomian [Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, 1994]. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.