Soliton topology versus discrete symmetry in optical lattices
  We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general ``charge rule'' using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing in the case of Bessel lattices allows us to derive also a overall stability rule for the allowed vortex solitons. 
Yaroslav V. Kartashov, Albert Ferrando, Alexey A. Egorov, and Lluis   Torner