Delocalization induced by nonlinearity in systems with disorder

We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice in time takes place with an algebraic growth of number of populated sites $\Delta n \propto t^{\nu}$. The numerical values of $\nu$ are found to be approximately $0.15 - 0.2$ and 0.25 for the dimension $d=1$ and 2 respectively being in a satisfactory agreement with the theoretical value $d/(3d+2)$. The localization is preserved below a certain critical value of nonlinearity. We also discuss the properties of the fidelity decay induced by a perturbation of nonlinear field.