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


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.

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Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Engineering & Applied Sciences > Electrical, Electronic & Power Engineering
Additional Information: © 2005, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Uncontrolled Keywords: Fokker-Planck equation,nonlinear optics,nonlinear oscillators,stochastic dynamics,Applied Mathematics,Statistical and Nonlinear Physics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2005-04-15
Authors: Prilepsky, Jaroslaw E. ( 0000-0002-3035-4112)
Derevyanko, Stanislav A.

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