Dynamic of one dimensional wave packet in high-order approximations of nonlinear dispersion theory

Abstract EN

We are interested by the solution state solutions of the higher order nonlinear Schrödinger equation which models the propagation of solutions in optical fibers.

This nonlinear wave equation is solved by using the coupled amplitude-phase formulation.

These gives rise to a coupled pair of equations, which describe the interaction and dynamics between the amplitude and the phase of the pulse.

Integrating one of them, a characteristic equation is derived.

For different particular cases of the dependent nonlinear parameters, various types of solution solutions are investigated.

In the absence of the third-order dispersion, we have obtained two different families of solutions : bright solution in anomalous-dispersion regime and dark solution in normal dispersion regime.

Other family of bright solutions which is characterized by a simple quadratic dependence of the solution phase on its amplitude is obtained when the third-order dispersion effect is zero.

It is specifically investigated the dynamics of solutions in the presence of third-order dispersion which is well described by the Korteweg-de Vries nonlinear equation.