Determination of Schrödinger nonlinearities from the scattering map
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866914043318501376 |
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| author | Killip, Rowan Murphy, Jason Visan, Monica |
| author_facet | Killip, Rowan Murphy, Jason Visan, Monica |
| contents | We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schrödinger solutions. We then solve this deconvolution problem using the Beurling--Lax Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determination of Schrödinger nonlinearities from the scattering map Killip, Rowan Murphy, Jason Visan, Monica Analysis of PDEs We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schrödinger solutions. We then solve this deconvolution problem using the Beurling--Lax Theorem. |
| title | Determination of Schrödinger nonlinearities from the scattering map |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.03218 |