Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds

Abstract

This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $\hat{I}\pm \in (\frac{1}{2},1)$ on any non-empty open subset of the underlying manifold determines the Riemannian metric, the drift and the potential, simultaneously and uniquely, up to a gauge transformation, under the same geometric assumptions on the observation set as in \cite{feizmohammadi2024calderonproblemfractionalschrodinger}. The method of proof is based on that of \cite{feizmohammadi2024calderonproblemfractionalschrodinger} for fractional Schrödinger operators, with the incorporation of the Runge approximation to recover the drift term.

A gap and some inacuracies in the previous version have been fixed