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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.19129 |
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| _version_ | 1866908283461173248 |
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| author | Lee, Zachary Pavlović, Nataša |
| author_facet | Lee, Zachary Pavlović, Nataša |
| contents | In this work, we address an inverse problem for a defocusing cubic nonlinear Schrödinger (NLS) equation in dimensions $d\in\{1, 2,3\}$ in a range of Sobolev spaces $H^s(\mathbb{R}^d)$ by employing the method of approximate solutions. We recover a smooth, space-dependent and compactly supported function $α$ that controls the nonlinearity (and thus self-interaction strength) in a multiplicative fashion. To the best of our knowledge, this is the first work based on approximate solutions in Sobolev spaces that treats an inverse problem for the NLS and provides explicit recovery of $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An inverse Problem for the cubic $α$-NLS in Sobolev spaces Lee, Zachary Pavlović, Nataša Analysis of PDEs In this work, we address an inverse problem for a defocusing cubic nonlinear Schrödinger (NLS) equation in dimensions $d\in\{1, 2,3\}$ in a range of Sobolev spaces $H^s(\mathbb{R}^d)$ by employing the method of approximate solutions. We recover a smooth, space-dependent and compactly supported function $α$ that controls the nonlinearity (and thus self-interaction strength) in a multiplicative fashion. To the best of our knowledge, this is the first work based on approximate solutions in Sobolev spaces that treats an inverse problem for the NLS and provides explicit recovery of $α$. |
| title | An inverse Problem for the cubic $α$-NLS in Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.19129 |