Do nonlinear waves in random media follow nonlinear diffusion equations?

Abstract

Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling. We discuss, analyze and compare nonlinear diffusion equations with compact or exponentially decaying interactions, and generalized dependences of the diffusion coefficient on the density. Our results strongly support applicability to wave packet spreading in disordered nonlinear lattices.