New bifurcation diagram in one model of vortex dynamics

We consider a completely Liouville-integrable Hamiltonian system with two degrees of freedom, which includes two limit cases. The first system describes the dynamics of two vortex filaments in a Bose–Einstein condensate enclosed in a harmonic trap. The second system governs the dynamics of point vortices in an ideal fluid in a circular domain. For the case of vortices with arbitrary intensities, we explicitly reduce the problem to a system with one degree of freedom. For intensities of different signs, we detect a new bifurcation diagram, which has not been previously encountered in works on this topic. Also, we obtain a separating curve, which is related to the change of the projections of Liouville tori without changing their number.