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Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schr{ö}dinger Lattice

P. G. Kevrekidis·B. A. Malomed·D. J. Frantzeskakis·R. Carretero-González
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Abstract

In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{ö}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.

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P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, R. Carretero-González. 2004-06-29. Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schr{ö}dinger Lattice. https://doi.org/10.1103/physrevlett.93.080403

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