Born and Inverse Born Series for a Special Case of the Second Harmonic Generation Problem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910776783011840 |
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| author | McNeill, Ross |
| author_facet | McNeill, Ross |
| contents | We study the Born and Inverse Born series for a special case of the second harmonic generation system of PDEs. We give a recursive formula for the forward operators and prove boundedness conditions that guarantee the convergence of the Born and inverse Born series. We also use fixed point theory to give explicit conditions for convergence of the Born series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Born and Inverse Born Series for a Special Case of the Second Harmonic Generation Problem McNeill, Ross Analysis of PDEs 35R30 (Primary) 45Q05 (Secondary) We study the Born and Inverse Born series for a special case of the second harmonic generation system of PDEs. We give a recursive formula for the forward operators and prove boundedness conditions that guarantee the convergence of the Born and inverse Born series. We also use fixed point theory to give explicit conditions for convergence of the Born series. |
| title | Born and Inverse Born Series for a Special Case of the Second Harmonic Generation Problem |
| topic | Analysis of PDEs 35R30 (Primary) 45Q05 (Secondary) |
| url | https://arxiv.org/abs/2412.13284 |