Anderson localization and shock waves in disordered media

Our contribution provides a review of the recent studies on wave propagation in disordered media in the linear and nonlinear regime. In particular, we reported the results of theoretical and experimental investigations aimed to understand, and eventually exploit, the mechanisms ruling the competition between nonlinear effects and disorder on the light propagation process in two particular cases. The former is more applicative, concerns the study of the non-linear propagation of light in a fiber that displays a structural disorder along the propagation direction. The second study deals with the emergence of optical shock waves in nonlinear systems in the presence of disorder. For both cases, we introduce the theoretical model developed to effectively introduce structural disorder into the nonlinear Schroedinger equation in order to provide analytical results in agreement with experimental observations.