Solitonization of the Anderson localization

Summary form only given. Disorder and nonlinearity sustain two different forms of wave-localization: Anderson states and solitary waves, respectively. Anderson states are given by the autostates with negative energy of a random potential, in absence of any form of nonlinearity; solitary waves, or solitons, are only due to nonlinearity. Nevertheless, these forms of wave trapping have several features in common, as for example the link between the localization length and the propagation constant, or eigenvalue. Experiments, either in nonlinear optics [1] or in dissipative random systems [2], recently addressed the effect of nonlinearity on the shape of disorder induced localization. Here we report on simple theoretical arguments that allow to describe the passage from Anderson states to solitons, beyond perturbation theory, when increasing the strength of nonlinearity. The theoretical analysis is confirmed by numerical simulations [3].