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, two new solution-type solutions have been presented for the Hirota equation used to describe the propagation of an ultrashort optical pulse in the context of long-distance optical fiber communications. The evolution of these pulses is calculated by means of the Anderson variational method coupled with the Runge– Kutta method of order 4 (RK4) using super-Gaussian and cosh-Gaussian pulses as test functions. The results obtained in this work show that the two solutions presented propagate without distortions and are temporally stable and can be used to overcome the effects of signal distortion in the context of very high data rate transmissions optical communications over homogeneous fiber. The results obtained also show that the central position of the pulse does not affect the dynamics of the different parameters and that only the soliton power and the linear momentum are conserved quantities. Moreover, it should be noted that that the choice between super-Gaussian and chirped cosh-Gaussian profiles has no obvious difference on the propagation dynamics of an ultrashort solitonic pulse in the context of long-haul optical fiber communications. The results of the current paper have not been widely reported before.