A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons

R. O. Moore, G. Biondini, W. L. Kath

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We describe in detail the application of importance sampling to numerical simulations of large noise-induced perturbations in soliton-based optical transmission systems governed by the nonlinear Schrödinger equation. The method allows one to concentrate the samples in Monte Carlo simulations around those noise realizations that are most likely to produce the large pulse deformations connected with errors, and it yields computational speedups of several orders of magnitude over standard Monte Carlo simulations. We demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude, frequency, timing, and phase fluctuations in a prototypical soliton-based communication system.

Original languageEnglish (US)
Pages (from-to)523-549
Number of pages27
JournalSIAM Review
Volume50
Issue number3
DOIs
StatePublished - Sep 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Importance sampling
  • Monte Carlo simulations
  • Noise
  • Nonlinear Schrödinger equation
  • Optical fibers
  • Solitons

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