Statistics of solitonbearing 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 nonGaussian) which are beyond perturbation theory. Our method is a development of the instanton formalism (method of optimal fluctuation) based on a saddlepoint 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).
 Publication:

Physical Review E
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevE.63.025601
 arXiv:
 arXiv:nlin/0004001
 Bibcode:
 2001PhRvE..63b5601F
 Keywords:

 42.65.Tg;
 05.40.Ca;
 05.45.Yv;
 42.81.Dp;
 Optical solitons;
 nonlinear guided waves;
 Noise;
 Solitons;
 Propagation scattering and losses;
 solitons;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 4 pages. Submitted to PRL