Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response

We study the effects of a delayed Raman response on soliton collisions in optical fibre transmission systems with multiple frequency channels. We show that the propagation of a given soliton undergoing many collisions with solitons from other frequency channels is described by a perturbed stochastic nonlinear Schrodinger equation, in which the stochastic perturbative terms are due to collision induced amplitude and frequency changes. Using the adiabatic perturbation theory we find that the distribution function of the soliton amplitude is lognormal, i.e. strongly non-Gaussian. The frequency of the soliton is also found to be a random variable that is not self-averaging. The results of our extensive numerical simulations incorporating the technique of importance sampling are in very good agreement with the theoretical predictions.