Propagation of nonlinear waves in disordered media

Abstract

We study propagation of stationary waves in disordered non-linear media described by the non-linear Schroedinger equation and show that for given boundary conditions and a given coherent wave incident on a sample the number of solutions of the equation increase exponentially with the sample size. We also discuss the ballistic case, the sensitivity of the solutions to a change of external parameters, the similarity of this problem to the problem of spin glasses and time-dependent solutions.