Screening and localization in the nonlinear Anderson problem

We study the spreading dynamics of an initially localized wave packet in 1D nonlinear Schr\"{o}dinger lattices with random potential. It is shown that adding small dielectric coupling to surrounding random medium results in asymptotic localization of the nonlinear field. The nonlinear localization length depends on dielectric loss of the medium at low temperatures and the value of nonlinearity parameter. The model predicts a possibility of self-induced localization when the ``medium" to which the wave field is dielectrically coupled is the nonlinear wave itself.