Multi solitons solutions of Korteweg de Vries (KdV) equation : six solitons

Abstract

The Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation has nonlinearity and dispersion effects. The balance between these effects leads to a wave propagation that is soliton solution. It propagates without changing it?s shape. The purpose of this research is to obtain the multi solitons solutions of KdV equation up to six-solitons solutions. The Hirota?s bilinear method will be implemented to find the explicit expression for up to six-solitons solutions of KdV equation. Identification of the phase shift that makes full interactions happens at ??=0 and ??=0 for each multi soliton solution of KdV equation. The Maple computer programming will be used to produce the various interactive graphical outputs for up to six-solitons solutions of KdV equation.