Stability of nonlinear recovery from scattering and modified scattering maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913799501512704 |
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| author | Chen, Gong Murphy, Jason |
| author_facet | Chen, Gong Murphy, Jason |
| contents | We prove stability estimates for the recovery of the nonlinearity from the scattering or modified scattering map for one-dimensional nonlinear Schrödinger equations. We consider nonlinearities of the form $a(x) |u|^p u$ for $p\in [2,4]$ and $[1+a(x)]|u|^2 u$, where $a$ is a localized function. In the first case, we show that for $p\in(2,4]$ we may obtain a Hölder-type stability estimate for recovery via the scattering map, while for $p=2$ we obtain a logarithmic stability estimate. In the second case, we show a logarithmic stability estimate for recovery via the modified scattering map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of nonlinear recovery from scattering and modified scattering maps Chen, Gong Murphy, Jason Analysis of PDEs We prove stability estimates for the recovery of the nonlinearity from the scattering or modified scattering map for one-dimensional nonlinear Schrödinger equations. We consider nonlinearities of the form $a(x) |u|^p u$ for $p\in [2,4]$ and $[1+a(x)]|u|^2 u$, where $a$ is a localized function. In the first case, we show that for $p\in(2,4]$ we may obtain a Hölder-type stability estimate for recovery via the scattering map, while for $p=2$ we obtain a logarithmic stability estimate. In the second case, we show a logarithmic stability estimate for recovery via the modified scattering map. |
| title | Stability of nonlinear recovery from scattering and modified scattering maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.13795 |