Bifurcations of Liouville Tori in a System of Two Vortices of Positive Intensity in a Bose–Einstein Condensate

Abstract

A completely Liouville integrable Hamiltonian system with two degrees of freedom that describes the dynamics of two vortex filaments in a Bose–Einstein condensate enclosed in a harmonic trap is considered. For a pair of vortices of positive intensity, a bifurcation of three Liouville tori into a single one is detected. Such a bifurcation was previously found in the Goryachev–Chaplygin–Sretensky integrable case in rigid body dynamics. For an integrable perturbation of the intensity ratio parameter, the identified bifurcation proves to be unstable, which leads to bifurcations of the type of two tori into one and vice versa.