Statistics of soliton-bearing systems with additive noise

Abstract

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though the noise is weak, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governed by a noisy nonlinear Schrödinger equation. We then apply our method to optical soliton transmission systems using signal control elements (filters and amplitude and phase modulators).