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Inverse problems for
nonlinear magnetic Schrödinger equations on conformally
transversally anisotropic manifolds
Katya Krupchyk and Gunther Uhlmann |
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Vol. 16 (2023), No. 8, 1825–1868
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Abstract |
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We study the inverse boundary problem for a nonlinear magnetic Schrödinger operator on a conformally transversally anisotropic Riemannian manifold of dimension . Under suitable assumptions on the nonlinearity, we show that the knowledge of the Dirichlet-to-Neumann map on the boundary of the manifold determines the nonlinear magnetic and electric potentials uniquely. No assumptions on the transversal manifold are made in this result, whereas the corresponding inverse boundary problem for the linear magnetic Schrödinger operator is still open in this generality. |
Keywords
inverse boundary problem, nonlinear Schrödinger equation,
conformally transversally anisotropic manifold, Gaussian
beams
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Mathematical Subject Classification
Primary: 35R30
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Milestones
Received: 2 February 2021
Revised: 26 October 2021
Accepted: 4 February 2022
Published: 16 October 2023
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Authors |
| Katya Krupchyk | |
| Department of Mathematics University of California Irvine, CA United States |
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| Gunther Uhlmann | |
| Department of Mathematics University of Washington Seattle, WA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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