Numerical Studying of Soliton in the Korteweg-de Vries (KdV) Equation

Abstract

In this paper, we use a numerical approach for finding soliton of the Korteweg-de Vries (KdV) equation in infinite dimensionalization. The traveling wave hypothesis is used to extract the analytic soliton solution of KdV equation. Barbera (1993) shown that KdV equation is a solution of Hamiltonian energy optimization in the level set of the momentum. We numerically solve the optimization problem by using steepest descent method and adding the assumption to guarantee the constraint will be fulfilled. From this method, the dynamic system of the problem is obtained and finite difference implementation is used for solving the dynamic system. Based on the method and the hypothesis, the soliton is obtained.