Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear   Schr{\"o}dinger Lattice
  In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{\"{o}}dinger equation, we find discrete vortex solitons with various values of the topological charge $S$. Stability regions for the vortices with $S=0,1,3$ are investigated. The S=2 vortex is unstable, spontaneously rearranging into a stable one with S=3. In a two-component extension of the model, we find a novel class of stable structures, consisting of vortices in the different components, perpendicularly oriented to each other. Self-localized states of the proposed types can be observed experimentally in Bose-Einstein condensates trapped in optical lattices, and in photonic crystals built of microresonators. 
P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis and R.   Carretero-Gonz\'alez