Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909696598736896 |
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| author | Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica |
| author_facet | Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica |
| contents | We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14571 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity Harrop-Griffiths, Benjamin Killip, Rowan Visan, Monica Analysis of PDEs We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space. |
| title | Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.14571 |