Long-range transmission of solitons in random media

A statistical approach of the propagation of solitons in media with spatially random perturbations is developed. applying the inverse scattering transform several regimes are put into evidence which are determined by the mass and the velocity of the incoming soliton and also by the correlation length of the perturbation. The mass of the transmitted soliton may tend to zero exponentially las a function of the size of the slab) or following a power law; or else the soliton may keep its mass if it is initially large enough, while its velocity decreases at a logarithmic rate or even slower. Numerical simulations are in good agreement with the theoretical results.