Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909606056296448 |
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| author | Avdonin, Sergei Mikhaylov, Alexander Mikhaylov, Victor Park, Jeff |
| author_facet | Avdonin, Sergei Mikhaylov, Alexander Mikhaylov, Victor Park, Jeff |
| contents | We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the dynamical Dirichlet--to--Neumann operator. We first provide a method to recover spectral data for an abstract system from dynamic data and apply it to the Schrödinger equation. We then develop a strategy for solving the inverse problem for the Schrödinger equation using this method with other techniques of the Boundary control method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential Avdonin, Sergei Mikhaylov, Alexander Mikhaylov, Victor Park, Jeff Analysis of PDEs Mathematical Physics We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the dynamical Dirichlet--to--Neumann operator. We first provide a method to recover spectral data for an abstract system from dynamic data and apply it to the Schrödinger equation. We then develop a strategy for solving the inverse problem for the Schrödinger equation using this method with other techniques of the Boundary control method. |
| title | Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2505.06142 |