Destruction of Anderson localization in nonlinear lattices

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We want to study how the localization properties of disordered lattices are modified by nonlinearity. Relevant experimental realizations of such systems include photonic lattices, Bose-Einstein condensate, and mechanical disordered systems. Two setups will be intensively studied numerically: (i) a spreading of an initially localized wave packet in a large lattice and (ii) a transmission through a nonlinear disordered layer. In the latter case we will perform a novel statistical bifurcation analysis to characterize statistically an expected sharp transition from static to time-dependent transmission. In both cases we expect to observe destruction of the localization by the nonlinearity, what should lead to an unbounded diffusion and to an enhanced transmission, respectively. We will statistically characterize these effects in dependence on the nonlinearity strength, length of the lattice, and other parameters.