Dynamics of the Optical Pulse in a Nonlinear Medium: Approach of Moment Method Coupled with the Fourth Order Runge-Kutta Method

Abstract

In this paper, we considered the nonlinear Schrodinger equation and applied the moment method ¨ in order to investigate the evolution of pulse parameters in nonlinear medium. This mathematical model described the effects of cubic nonlinear and the nonlinear dispersion terms on the soliton.  The application of the moment method leads to variational equations that is integrated numerically by the fourth order Runge-Kutta method. The results obtained shows the variations of some important parameters of the pulse namely the energy, the pulse position, the frequency shift, the chirp and the width. It reveals the effects of the nonlinear dispersion and nonlinear cubic terms on each parameter on the pulse. The moment method is appropriate to study the dynamics of the optical pulse in a nonlinear medium modelled by the nonlinear Schrodinger equation.