Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium

This is the first study of one of the transmission problems associate to the non-linear Schrödinger equation with a random potential. We show that for almost every realization of the medium the rate of transmission vanishes when increasing the size of the medium; however, whereas it decays exponentially in the linear regime, it decays polynomially in the nonlinear one.This work is part of a Thèse de Troisième Cycle by P. Devillard.⁽⁶⁾