Unique determination for an inverse problem from the vortex dynamics

We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct a real-analytic potential by measuring the entrance and exit positions as well as travel times between boundary points. In particular, the work removes the flatness assumption on the potential from the earlier result. A key step of our method is a constructional procedure of recovering the boundary jet of the potential.

Automated summary

In this study, we investigate the reconstruction of a background potential from the dynamical behavior of a vortex dipole. We prove that, under suitable conditions, a real-analytic potential can be uniquely reconstructed by measuring entrance and exit positions, as well as travel times between boundary points. Importantly, this work eliminates the flatness assumption on the potential from previous results, with a key step involving a constructional procedure for recovering the boundary jet of the potential.