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

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

2004-09-23

arxiv.org/abs/nlin/0409048v1

Physica D 203 (2005) 249-269

Nonlinear Sciences

Chaotic Dynamics

29 pages, no figures, submitted to Physica D

Scientific paper

10.1016/j.physd.2005.04.004

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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