Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity

Jaroslaw E. Prilepsky; Stanislav A. Derevyanko

doi:10.1016/j.physd.2005.04.004

Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity

Jaroslaw E. Prilepsky, Stanislav A. Derevyanko^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength.

Original language	English
Pages (from-to)	249-269
Number of pages	21
Journal	Physica D
Volume	203
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physd.2005.04.004
Publication status	Published - 15 Apr 2005

Bibliographical note

Keywords

Fokker-Planck equation
nonlinear optics
nonlinear oscillators
stochastic dynamics

Access to Document

10.1016/j.physd.2005.04.004

Statistics of noise-driven coupled nonlinear oscillators
© 2005, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 280 KBLicence: CC BY-NC-ND 3.0

Cite this

@article{796dedbe3b5f4079a297087ad191b7f4,

title = "Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity",

abstract = "We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength.",

keywords = "Fokker-Planck equation, nonlinear optics, nonlinear oscillators, stochastic dynamics",

author = "Prilepsky, {Jaroslaw E.} and Derevyanko, {Stanislav A.}",

note = "{\textcopyright} 2005, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/",

year = "2005",

month = apr,

day = "15",

doi = "10.1016/j.physd.2005.04.004",

language = "English",

volume = "203",

pages = "249--269",

journal = "Physica D",

issn = "0167-2789",

publisher = "Elsevier",

number = "3-4",

}

TY - JOUR

T1 - Statistics of noise-driven coupled nonlinear oscillators

T2 - applications to systems with Kerr nonlinearity

AU - Prilepsky, Jaroslaw E.

AU - Derevyanko, Stanislav A.

PY - 2005/4/15

Y1 - 2005/4/15

N2 - We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength.

AB - We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength.

KW - Fokker-Planck equation

KW - nonlinear optics

KW - nonlinear oscillators

KW - stochastic dynamics

UR - http://www.scopus.com/inward/record.url?scp=18244365583&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2005.04.004

DO - 10.1016/j.physd.2005.04.004

M3 - Article

AN - SCOPUS:18244365583

SN - 0167-2789

VL - 203

SP - 249

EP - 269

JO - Physica D

JF - Physica D

IS - 3-4

ER -

Statistics of noise-driven coupled nonlinear oscillators: applications to systems with Kerr nonlinearity

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this