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

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.