Partially coherent waves in nonlinear periodic lattices

We study the propagation of partially coherent (random-phase) waves in nonlinear periodic lattices. The dynamics in these systems is governed by the threefold interplay between the nonlinearity, the lattice properties, and the statistical (coherence) properties of the waves. Such dynamic interplay is reflected in the characteristic properties of nonlinear wave phenomena (e.g., solitons) in these systems. While the propagation of partially coherent waves in nonlinear periodic systems is a universal problem, we analyze it in the context of nonlinear photonic lattices, where recent experiments have proven their existence.