Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method

In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the nonlinear dispersive KdV equation with initial profile. The approach rests mainly on Adomian decomposition method. The single soliton, the two-soliton and rational solutions are obtained by this method. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.