Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential

TL;DR

This paper investigates vortex families near spectral edges in the Gross-Pitaevskii and discrete nonlinear Schrödinger equations with periodic potentials, revealing families that extend to the band edges and those that terminate earlier.

Contribution

It numerically demonstrates the existence of vortex families that either terminate near or extend all the way to the band edges in these nonlinear equations.

Findings

Vortex families exist near spectral band edges.

Some vortex families terminate before reaching the edges.

Other vortex families extend continuously to the band edges.

Abstract

We examine numerically vortex families near band edges of the Bloch wave spectrum in the Gross--Pitaevskii equation with a two-dimensional periodic potential and in the discrete nonlinear Schroedinger equation. We show that besides vortex families that terminate at a small distance from the band edges via fold bifurcations there exist vortex families that are continued all way to the band edges.