High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915811929620480 |
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| author | Jendrej, Jacek Salvi, Tony |
| author_facet | Jendrej, Jacek Salvi, Tony |
| contents | We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we establish global existence of solution together with persistence of the localization of the associated profile. We further provide a rigorous derivation of the asymptotic expansion at arbitrary order of such solutions, taking into account long-range effects induced by the cubic component of the nonlinearity. Our analysis relies on the space-time resonance method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19374 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation Jendrej, Jacek Salvi, Tony Analysis of PDEs Quantum Physics We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we establish global existence of solution together with persistence of the localization of the associated profile. We further provide a rigorous derivation of the asymptotic expansion at arbitrary order of such solutions, taking into account long-range effects induced by the cubic component of the nonlinearity. Our analysis relies on the space-time resonance method. |
| title | High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation |
| topic | Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/2602.19374 |