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Title: Noise-induced perturbations of dispersion-managed solitons

Abstract

We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems.

Authors:
; ;  [1]
  1. Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260 (United States)
Publication Date:
OSTI Identifier:
20982594
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.053818; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DENSITY; DISTURBANCES; LASER RADIATION; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NOISE; NONLINEAR PROBLEMS; OPTICAL FIBERS; PERTURBATION THEORY; PROBABILITY; SCHROEDINGER EQUATION; SIMULATION; SOLITONS; TRANSMISSION; TRAVELLING WAVES

Citation Formats

Li, Jinglai, Spiller, Elaine, and Biondini, Gino. Noise-induced perturbations of dispersion-managed solitons. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.053818.
Li, Jinglai, Spiller, Elaine, & Biondini, Gino. Noise-induced perturbations of dispersion-managed solitons. United States. doi:10.1103/PHYSREVA.75.053818.
Li, Jinglai, Spiller, Elaine, and Biondini, Gino. Tue . "Noise-induced perturbations of dispersion-managed solitons". United States. doi:10.1103/PHYSREVA.75.053818.
@article{osti_20982594,
title = {Noise-induced perturbations of dispersion-managed solitons},
author = {Li, Jinglai and Spiller, Elaine and Biondini, Gino},
abstractNote = {We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems.},
doi = {10.1103/PHYSREVA.75.053818},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}