 
Summary: Statistics of solitonbearing systems with additive noise
G. E. Falkovich,1,2
I. Kolokolov,1,3
V. Lebedev,1,4
and S. K. Turitsyn5
1
Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
2
Institute for Theoretical Physics, University of California, Santa Barbara, California 931064030
3
Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
4
Landau Institute for Theoretical Physics, Moscow, Kosygina 2, 117940, Russia
5
Photonics Research Group, Aston University, Birmingham B4 7ET, United Kingdom
Received 22 March 2000; published 18 January 2001
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 nonGaussian which are beyond perturbation theory. Our method is a development of the instanton
formalism method of optimal fluctuation based on a saddlepoint approximation in the path integral. We first
