Soliton solutions of KdV equation

Abstract

One of the most popular soliton equations is the Korteweg de Vries (KdV) equation which is usually used to model shallow water waves. The general forms of this equation is given by 06=++xxxxtuuuu where u(x,t) describes the elongation of the wave at distance x and time t. The second and third term and represent the nonlinear effects of this equation. In this work, KdV equation will be solved using method of separation variable. Then the solution obtained will be simulated for n-soliton solution for KdV equation using Mathematica software.