Hirota bilinear computation of multi soliton solutions korteweg de vries equation

Abstract

Soliton is the solution of nonlinear partial differential equation that exists due to the balance between nonlinearity and dispersive effects. The existence of these two effects in Korteweg de Vries (KdV) equation enables us to obtain solitons solutions. The purpose of this research is to obtain the multi soliton solutions of KdV equation by using Hirota bilinear method. This method can produce the explicit expression for soliton solutions of KdV equation. From these solutions, a general pattern of F function in Hirota bilinear method is revealed. The amplitude of interacting soliton will determine the phase shift pattern. Various interactive graphical outputs produced by MAPLE computer programming can illustrate the solutions of these multi soliton up to eight-soliton solutions of KdV equation.