(untitled) (Sciences & Technology. A, exactes sciences, 2004)
We are interested by the soliton state solutions of the higher order nonlinear Schrödinger equation which models the propagation of solitons 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 soliton solutions are investigated. In the absence of the third-order dispersion, we have obtained two different families of solitons: bright soliton in anomalous-dispersion regime and dark soliton in normal dispersion regime. Other family of bright solitons which is characterized by a simple quadratic dependence of the soliton phase on its amplitude, is obtained when the third-order dispersion effect is zero. It is specifically investigated the dynamics of solitons in the presence of third-order dispersion which is well described by the Korteweg-de Vries nonlinear equation.