# Symmetry-breaking instability of leapfrogging vortex rings in a Bose-Einstein condensate

## TL;DR

This paper investigates the instability of leapfrogging vortex rings in a Bose-Einstein condensate, revealing how symmetry-breaking deformations lead to aperiodic dynamics and depend on initial configurations.

## Contribution

It demonstrates the dynamical instability of coaxial vortex rings and analyzes the dependence of this instability on initial arrangements using theoretical models.

## Key findings

- Vortex rings are unstable against symmetry-breaking deformations.
- Instability varies significantly with initial vortex configurations.
- The study uses Gross-Pitaevskii and vortex-filament models for analysis.

## Abstract

Three coaxial quantized vortex rings in a Bose-Einstein condensate exhibit aperiodic leapfrogging dynamics. It is found that such circular vortex rings are dynamically unstable against deformation breaking axial rotational symmetry. The dynamics of the system are analyzed using the Gross-Pitaevskii and vortex-filament models. The dependence of the instability on the initial arrangement of the vortex rings is investigated. The system is found to be significantly unstable for a specific configuration of the three vortex rings.