Power-dependent shaping of vortex solitons in optical lattices with   spatially modulated nonlinear refractive index
  We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out-of-phase the competition between both effects results in remarkable shape transformations of the solitons which profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth. 
Yaroslav V. Kartashov, Victor A. Vysloukh, Lluis Torner