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 Schrödinger equation 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 the amplitudes of the random fluctuations go to zero and the size of the 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 following a power law, or else the soliton may keep its mass, while its velocity decreases at a logarithmic rate or even more slowly. Numerical simulations are in good agreement with the theoretical results.

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