  Completely Liouville integrable Hamiltonian system with two degrees of
freedom, describing the dynamics of two vortex filaments in a Bose-Einstein
condensate enclosed in a cylindrical trap, is considered. For the system of two
vortices with identical intensities detected bifurcation of three Liouville
tori into one. Such a bifurcation was found in the integrable case of
Goryachev-Chaplygin-Sretensky in the rigid body dynamics.
