Inverse problem for fractional Schr\"{o}dinger equations with drift on closed Riemannian manifolds

Tianyu Cai; Xi Chen

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arXiv · 2508.16879

Inverse problem for fractional Schr\"{o}dinger equations with drift on closed Riemannian manifolds

Tianyu Cai·Xi Chen

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Abstract

This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $\alpha\in (\frac{1}{2},1)$ 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 Schr\"{o}dinger operators, with the incorporation of the Runge approximation to recover the drift term.

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Tianyu Cai, Xi Chen. 2025-08-23. Inverse problem for fractional Schr\"{o}dinger equations with drift on closed Riemannian manifolds. https://arxiv.org/abs/2508.16879

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