A numerical solution to the Zakharov-Shabat inverse scattering problem with application to solitary wave propagation in nonlinear optical fibers
(EN)
Frangos, P
(EN)
A new numerical solution which uses leapfrogging in space and time is developed in this work in order to solve coupled Gel'fand-Levitan-Marchenko integral equations in their general form, appearing in the formulation of the Zakharov-Shabat coupled-mode inverse scattering problem. As an application, the problem of solitary wave (pulse) propagation in a nonlinear optical fiber is implemented using the method developed here, since the envelope of the propagating solitary wave is found to satisfy the nonlinear (cubic) Schrödinger equation. It is found that the proposed method for the solitary wave calculation, based on the inverse scattering integral formulation, is very efficient and accurate, especially in the late-time period, where traditional methods based on the direct numerical solution of the corresponding nonlinear partial differential equation become inaccurate.
(EN)
