ASYMPTOTIC TRANSMISSION OF SOLITONS THROUGH RANDOM-MEDIA

This paper contains a study of the transmission of a soliton through a slab of nonlinear and random media. A random nonlinear Schrodinger eq uation is considered, where the randomness holds in the potential and the nonlinear coefficient. Using the inverse scattering transform, we exhibit several asymptotic behaviors corresponding to the limit when t he amplitudes of the random fluctuations go to zero and the size of th e slab goes to infinity. The mass of the transmitted soliton may tend to zero exponentially (as a function of the size of the slab) or follo wing a power law, or else the soliton may keep its mass, while its vel ocity decreases at a logarithmic rate or even more slowly. Numerical s imulations are in good agreement with the theoretical results.