Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schrödinger Lattice (original) (raw)

In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schrödinger 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.