• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Statistics of soliton-bearing systems with additive noise

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2001. Vol. 63. No. 025601(R). P. 025601-1-025601-4.
Kolokolov I., Lebedev V., Turitsyn S. K., Falkovich G. E.
We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though the noise is weak, we are interested in probabilities of large fluctuations ~generally non-Gaussian! which are beyond perturbation theory. Our method is a development of the instanton formalism ~method of optimal fluctuation! based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governed by a noisy nonlinear Schro¨dinger equation. We then apply our method to optical soliton transmission systems using signal control elements ~filters and amplitude and phase modulators!.