Vortex Splitting in Subcritical Nonlinear Schrodinger Equation

TL;DR

This paper investigates vortex dynamics in subcritical nonlinear Schrödinger equations, revealing how negative and varying pressures can cause vortex splitting, with implications for superfluid systems and Bose-Einstein condensates.

Contribution

It introduces the effects of negative pressure on vortex stability and demonstrates vortex ring splitting under periodic pressure variations in a nonlinear Schrödinger framework.

Findings

Identified critical pressure for vortex instability.

Calculated energies and velocities of vortices and rings.

Showed vortex splitting under periodic pressure changes.

Abstract

Vortices and axisymmetric vortex rings are considered in the framework of the subcritical nonlinear Schrodinger equations. The higher order nonlinearity present in such systems models many-body interactions in superfluid systems and allows one to study the effects of negative pressure on vortex dynamics. We find the critical pressure for which the straight-line vortex becomes unstable to radial expansion of the core. The energy of the straight-line vortices and energy, impulse and velocity of vortex rings are calculated. The effect of a varying pressure on the vortex core is studied. It is shown that under the action of the periodically varying pressure field a vortex ring may split into many vortex rings and the conditions for which this happens are elucidated. These processes are also relevant to experiments in Bose-Einstein condensates where the strength and the sign of two-body interactions can be changed via Feshbach resonance.