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

TL;DR

This paper investigates three-dimensional discrete vortex solitons in a nonlinear lattice model, analyzing their stability, transformations, and novel multi-component structures with potential experimental realizations.

Contribution

It introduces new stable vortex configurations and analyzes their stability in a 3D discrete nonlinear Schrödinger lattice, including multi-component vortex structures.

Findings

Stable vortex solitons with S=0,1,3 identified

S=2 vortex is unstable and transforms into S=3

Novel stable multi-component vortex structures discovered

Abstract

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.