Periodic orbits of Gross-Pitaevskii in the disc with vortices following point vortex flow (Q2403760)

This paper deals with the study of the Gross-Pitaevskii equations with small positive parameter. The author is interested in relative equilibria with vortices of degree \(\pm 1\) and in the existence of non-constant time periodic vortex solutions. The main result of the present paper covers the case of relative equilibria with a single vortex ring containing vortices of degree either 1 or \(-1\), but not both. The proof combines a constrained minimization method with topological minimax techniques, applied to a formulation of the problem within a rotational ansatz. The constrained minimization step involves minimizing the Ginzburg-Landau energy within a fixed symmetry class.