  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. 
Phase Topology of Two Vortices of the Identical Intensities in   Bose-Einstein Condensate