Spatial Localization of Nonlinear Waves in Layered and Modulated Media

We describe analytically the nonlinear dynamics of the stationary waves propagating in an anharmonic medium along layered or modulated periodic waveguide system. The exact dynamical equations for discrete systems of coupled anharmonic oscillators, which are typically used for the description of real experiments on the localization of powerful optical fluxes, are analytically derived on the microscopic level and the conditions of their applicability are obtained. The criterion of the appearance of a spatially localized state in such systems is derived.