Destruction of Anderson localization by a weak nonlinearity

We study numerically the spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrodinger 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 proportional to t(alpha), with the exponent alpha being in the range 0.3-0.4. For small nonlinearities the distribution remains localized in a way similar to the linear case.