Propagation of solitons in a randomly perturbed Ablowitz-Ladik chain

This paper deals with the transmission of a soliton in a discrete, nonlinear, and random medium. A random lattice nonlinear Schrödinger equation is considered, where the randomness holds in the on-site potential or in the coupling coefficients. We study the interplay of nonlinearity, randomness, and discreteness. We derive effective evolution equations for the soliton parameters by applying a perturbation theory of the inverse scattering transform and limit theorems of stochastic calculus.