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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/2509.25971 |
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| _version_ | 1866911185788469248 |
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| author | Oksanen, Lauri Zhang, Ruochong |
| author_facet | Oksanen, Lauri Zhang, Ruochong |
| contents | This paper recovers Hermitian connections of semi-linear wave equations with cubic nonlinearity. The main novelty is in the geometric generality: we treat the case of an arbitrary globally hyperbolic Lorentzian manifold. Our approach is based on microlocal analysis of nonlinear wave interactions, which recovers a non-abelian broken light-ray transform, and the inversion of broken light-ray transforms on globally hyperbolic Lorentzian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse problem for connections in semi-linear wave equations on Lorentzian manifolds Oksanen, Lauri Zhang, Ruochong Analysis of PDEs This paper recovers Hermitian connections of semi-linear wave equations with cubic nonlinearity. The main novelty is in the geometric generality: we treat the case of an arbitrary globally hyperbolic Lorentzian manifold. Our approach is based on microlocal analysis of nonlinear wave interactions, which recovers a non-abelian broken light-ray transform, and the inversion of broken light-ray transforms on globally hyperbolic Lorentzian manifolds. |
| title | Inverse problem for connections in semi-linear wave equations on Lorentzian manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.25971 |