Disordered Nonlinear Schroedinger Equation

Here, we deal with the nonlinear Schroedinger equation in the presence of structural disorder. The strength of disorder allows the formation of light localizations, the Anderson states. The effect of focusing and defocusing nonlinearities, present in the model equation, on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential. We find closed form expressions showing that nonlocality stabilizes Anderson states. Numerical analysis validates the theoretical results. A regime in which multiple Anderson localizations are excited and compete by nonlocality is also outlined.