DYNAMIC OF ONE DIMENSIONAL WAVE PACKET IN HIGH-ORDER APPROXIMATIONS OF NONLINEAR DISPERSION THEORY (Sciences & Technology. A, exactes sciences, 2004)
We are interested by the soliton state solutions of the higher order nonlinear Schrödinger equation whichmodels the propagation of solitons in optical fibers. This nonlinear wave equation is solved by using the coupledamplitude-phase formulation. These gives rise to a coupled pair of equations, which describe the interaction anddynamics between the amplitude and the phase of the pulse. Integrating one of them, a characteristic equation isderived. For different particular cases of the dependent nonlinear parameters, various types of soliton solutionsare 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 ofbright solitons which is characterized by a simple quadratic dependence of the soliton phase on its amplitude, isobtained when the third-order dispersion effect is zero. It is specifically investigated the dynamics of solitons inthe presence of third-order dispersion which is well described by the Korteweg-de Vries nonlinear equation.