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Three-dimensional solitary waves and vortices in a discrete nonlinear Schrödinger lattice
P G Kevrekidis1, B A Malomed, D J Frantzeskakis
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA.
Abstract:
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 and may 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.
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