Analysis for a two-step dispersion scheme for coupled non-linear Schrödinger equations

A model for the evolution of envelope waves in non-linear dispersive media is analyzed. With the help of coupled Non-Linear Schrödinger Equations (NLSE), the Modulation Instability (MI) of electromagnetic waves with periodic dispersion is investigated. A mathematical formulation is also derived for the MI gain. The analytical predictions are confirmed with numerical simulations of coupled NLSE with periodic constants.