Importance sampling for dispersion-managed solitons

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest-large phase or amplitude variations-are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that these small changes should be distributed in order to create a large, sought-after amplitude or phase change. Both steps are formulated and solved in terms of a variational problem. In addition, the first step makes use of the results of pertu rbation theory for dispersion-managed systems recently developed by the authors. We demonstrate this method by reconstructing the probability density function of amplitude and phase deviations of noise-perturbed dispersion-managed solitons and comparing the results to those of the original, unaveraged system.