# Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links

## TL;DR

This paper investigates the existence and stability of vortex knots in three-dimensional lattices of nonlinear oscillators with space-varying coupling, using theoretical analysis and numerical simulations.

## Contribution

It introduces a discrete model demonstrating that vortex knots can persist for long times in 3D oscillator arrays with tuned weak links.

## Key findings

- Vortex knots can exist for tens of vortex turnover periods.
- Theoretical and numerical analysis confirms long-term stability.
- Space-varying links enable complex vortex structures.

## Abstract

Quantized vortices in a complex wave field described by a defocusing nonlinear Schr\"odinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many tens of typical vortex turnover periods.