## Abstract

We demonstrate in detail the application of importance sampling to the numerical simulation of large noise-induced perturbations in soliton-based optical transmission systems governed by the nonlinear Schrödinger equation. The method allows one to concentrate numerical Monte Carlo simulations around the noise realizations that are most likely to produce the large pulse deformations connected with errors, and 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, and timing fluctuations in a prototypical soliton-based communication system.

Original language | English (US) |
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Pages (from-to) | 1418-1439 |

Number of pages | 22 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 67 |

Issue number | 5 |

DOIs | |

State | Published - 2007 |

## All Science Journal Classification (ASJC) codes

- Applied Mathematics

## Keywords

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