Pulse propagation in media with deterministic and random dispersion variations

We obtain a widely valid description of pulse broadening in dispersion-managed fiber with a random component in the dispersion. For short distances, a quasi-linear approach in the form of a simple perturbation expansion suffices to capture the broadening for each realization of the random dispersion. For intermediate distances, over which the noise and nonlinearity interact, we demonstrate that the partial differential equation can be reduced to a relatively simple system of nonlinear stochastic ordinary differential equations. Finally, we demonstrate that, over long distances, the slow evolution of the pulse width can be obtained by applying an appropriate multiple-scales averaging procedure to yield a new, scaled noise process effecting pulse broadening.