This theoretical work studies the role of detuning in the dynamics of Rabi vortices, i.e., vortices oscillating in the photonic and excitonic fields due to light-matter coupling, as introduced in Ref.  (note that the report itself was published after this analysis, in which it appears as arXiv:1801.02580).
Besides focusing on detuning, the Authors also describe the dynamics of the core through the effect of a Magnus force, acting on an effective particle (the latter idea also being a concept previously introduced by our broader collaboration). They find the mass (negative) to also depend on time. The spatial trajectories are simple (circle) but their temporal profile is more complex (featuring accelerations) and all this is accounted for by their description. They also introduce a "Rabi energy" (Eq. (12)) obtained through the overlap of the excitonic and photonic fields, and that depends on the position of the cores, and whose gradient, for vortices-positions as variables, defines another relevant force.
They solve the dynamics using a spectral method, meaning they do so through the introduction of a basis of special functions (Eqs. (5,6)), which involves a truncation that was checked numerically.