Surface lattice solitons in diffusive nonlinear media
  We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetric diffusion nonlinearity. Such solitons exist only in finite gaps of lattice spectrum. In contrast to latticeless geometries, where surface waves exist only when nonlinearity deflects light towards the material surface, the surface lattice solitons exist in settings where diffusion would cause beam bending against the surface. 
Yaroslav V. Kartashov, Victor A. Vysloukh, Lluis Torner