Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion

We study modulational instability (MI) in optical fibers with random group-velocity dispersion (GVD). consider Gaussian and dichotomous colored stochastic processes. resort to different analytical methods (namely, the cumulant expansion functional approach) assess their reliability estimating MI gain of origin. If power spectral density (PSD) GVD fluctuations is centered at null wave number, we obtain low-frequency sidelobes which converge those given by a white-noise perturbation when correlation length tends 0. instead processes are modulated space, one or more sidelobe pairs corresponding well-known parametric resonance (PR) condition can be found. A transition from small broad peaks nearly indistinguishable PR-MI predicted, limit large amplitudes lengths process. find that provides good estimates for PSD values lengths, very small. The approach rigorous only processes, but allows us model wider range parameters predict existence comparable observed homogeneous anomalous GVD.