Document Type

Article

Language

eng

Format of Original

30 p.

Publication Date

Spring 2010

Publisher

Society for Industrial and Applied Mathematics

Source Publication

Journal of Applied Dynamical Systems

Source ISSN

1536-0040

Original Item ID

doi: 10.1137/090761677

Abstract

The dispersion-managed nonlinear Schrödinger (DMNLS) equation governs the long-term dynamics of systems which are subject to large and rapid dispersion variations. We present a method to study large, noise-induced amplitude and phase perturbations of dispersion-managed solitons. The method is based on the use of importance sampling to bias Monte Carlo simulations toward regions of state space where rare events of interest—large phase or amplitude variations—are most likely to occur. Implementing the method thus involves solving two separate problems: finding the most likely noise realizations that produce a small change in the soliton parameters, and finding the most likely way that these small changes should be distributed in order to create a large, sought-after amplitude or phase change. Both steps are formulated and solved in terms of a variational problem. In addition, the first step makes use of the results of perturbation theory for dispersion-managed systems recently developed by the authors. We demonstrate this method by reconstructing the probability density function of amplitude and phase deviations of noise-perturbed dispersion-managed solitons and comparing the results to those of the original, unaveraged system.

Comments

Published version. Journal of Applied Dynamical Systems, Vol. 9, No. 2 (Spring 2010) 432-461. DOI. © 2010 Society for Industrial and Applied Mathematics. Used with permission.

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