Destruction of Anderson localization by a weak nonlinearity

We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schr"odinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $ \propto t^\alpha$,withtheexponent$\alpha$beingintherange$0.3 - 0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.