Eventual periodicity of forced oscillations of the Korteweg-de Vries type equation

In this paper, we study the eventual periodicity of the initial boundary value problem (IBVP) for Korteweg-de Vries equation posed on a bounded domain. We show that if the boundary forcing is periodic of period τ, then the solution u of the IBVP at each spatial point becomes eventually time-periodic of period τ. In order to exhibit eventual periodicity, we approximate the solution of the IBVP using the Adomian decomposition method. We compare our work with the approximate solution of IBVP obtained by the homotopy perturbation method and present numerical experiments using Mathematica.