Statistics of soliton-bearing systems with additive noise - art. no. 025601

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