Superfluid vortex multipoles and soliton stripes on a torus

TL;DR

This paper investigates vortex multipoles and soliton stripes on a torus within the nonlinear Schrödinger equation framework, identifying stable configurations and comparing full and reduced models to understand their dynamics and stability.

Contribution

It introduces a comprehensive analysis of vortex dipole and quadrupole configurations on a torus, including stability windows and the connection to soliton stripes, using both full and reduced models.

Findings

Identified stable and unstable vortex configurations on a torus.

Compared full NLS and reduced point-vortex models with high agreement.

Mapped stability windows for various vortex multipoles.

Abstract

We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schr\"odinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.