Generation and Propagation of Waves Train Induced by Modulational Instability  in Optical Communication Systems with Variable Dispersion and Nonlinearity

We start with the Coupled Nonlinear Schr\"odinger Equation, whose dispersion and nonlinear coefficients vary on time, into which we inject plane waves accompanied by infinitesimal perturbations. Under certain conditions we have established, these waves can fragment and form wave packets, the final outcome of which is the formation of salitary waves. This occurs at certain frequencies that depend on the characteristic of the propagation medium and which we call modulational instability zones. We have also shown the time interval for which this phenomenon appears. Numerical simulations have been made to make our investigations more believable. Their main application can be found in telecommunication systems, particularly in the information transmission through optical fiber.