On one unstable bifurcation in the dynamics of vortex structure

TL;DR

This paper investigates a specific unstable bifurcation in the vortex dynamics of a Bose-Einstein condensate, revealing how bifurcations of Liouville tori occur and their instability under perturbations.

Contribution

It identifies and analyzes an unstable bifurcation of Liouville tori in a Hamiltonian system modeling vortex dynamics, extending understanding of bifurcations in integrable systems.

Findings

Bifurcation of three Liouville tori into one was observed.

The bifurcation is unstable under parameter perturbations.

Perturbations cause bifurcations of two tori into one and vice versa.

Abstract

In this paper we consider a completely Liouville integrable Hamiltonian system with two degrees of freedom, which describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap. For vortex pairs of positive intensity detected bifurcation of three Liouville tori into one. Such bifurcation was found in the integrable case of Goryachev-Chaplygin-Sretensky in the dynamics of a rigid body. For the integrable perturbation of the physical parameter of the intensity ratio, identified bifurcation proved to be unstable, which led to bifurcations of the type of two tori into one and vice versa.