Do nonlinear waves in random media follow nonlinear diffusion equations?
  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. 
T. V. Laptyeva, J. D. Bodyfelt, and S. Flach
nlin.CD cond-mat.other