On numerical soliton solution of the Kaup–Kupershmidt equation and convergence analysis of the decomposition method

In this paper, we use the Adomian decomposition method (ADM) for obtaining soliton solution of the Kaup–Kupershmidt (KK) equation. We prove the convergence of this method applied to the nonlinear Kaup–Kupershmidt equation. The solution is found as an infinite series quickly converging to accurate solutions. The results of numerical examples are presented and only few terms are required to obtain accurate solutions. Most of the symbolic and numerical computations have been performed using the Computer Algebra System—Mathematica.