A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons

We describe in detail the application of importance sampling to numerical simulations of large noise-induced perturbations in soliton-based optical transmission systems governed by the nonlinear Schrödinger equation. The method allows one to concentrate the samples in Monte Carlo simulations around those noise realizations that are most likely to produce the large pulse deformations connected with errors, and it yields computational speedups of several orders of magnitude over standard Monte Carlo simulations. We demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude, frequency, timing, and phase fluctuations in a prototypical soliton-based communication system.