Soliton broadening under random dispersion fluctuations: Importance sampling based on low-dimensional reductions

We demonstrate that dispersion-managed solitons are less likely to experience critical broadening under the influence of random dispersion fluctuations than are solitons of the integrable nonlinear Schrödinger equation, and that this robustness increases with map strength from the constant-dispersion (integrable) limit to the large-map-strength limit. To achieve this, we exploit a separation of scales in dispersion-managed soliton dynamics to implement an importance-sampled Monte Carlo approach that determines the probability of rare broadening events. This approach reconstructs the tails (i.e., the regions of practical importance) of probability distribution functions with an efficiency that is several orders of magnitude greater than conventional Monte Carlo simulations. We further show that the variational approach with an appropriately scaled ansatz is surprisingly good at capturing the effect of random dispersion on pulse broadening; where it fails, it can still be used to guide very efficient simulation of the original equation.