Recovery of the nonlinearity from the modified scattering map
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909425616289792 |
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| author | Chen, Gong Murphy, Jason |
| author_facet | Chen, Gong Murphy, Jason |
| contents | We consider a class of one-dimensional nonlinear Schrödinger equations of the form \[ (i\partial_t+Δ)u = [1+a]|u|^2 u. \] For suitable localized functions $a$, such equations admit a small-data modified scattering theory, which incorporates the standard logarithmic phase correction. In this work, we prove that the small-data modified scattering behavior uniquely determines the inhomogeneity $a$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01455 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Recovery of the nonlinearity from the modified scattering map Chen, Gong Murphy, Jason Analysis of PDEs We consider a class of one-dimensional nonlinear Schrödinger equations of the form \[ (i\partial_t+Δ)u = [1+a]|u|^2 u. \] For suitable localized functions $a$, such equations admit a small-data modified scattering theory, which incorporates the standard logarithmic phase correction. In this work, we prove that the small-data modified scattering behavior uniquely determines the inhomogeneity $a$. |
| title | Recovery of the nonlinearity from the modified scattering map |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.01455 |