On small energy solutions of the Nonlinear Schrödinger Equation in 1D with a generic trapping potential with a single eigenvalue
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917790627135488 |
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| author | Cuccagna, Scipio Maeda, Masaya |
| author_facet | Cuccagna, Scipio Maeda, Masaya |
| contents | We prove in dimension $d=1$ a result similar to Soffer and Weinstein Jour. Diff. Eq. 98 (1992) capturing for pure power nonlinearities the whole range of exponents $p>1$. The proof is based on the virial inequality of Kowalczyk \textit{et al.} J. Eur. Math. Soc. (JEMS) 24 (2022) with smoothing estimates like in Mizumachi J. Math. Kyoto Univ. 48 (2008). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On small energy solutions of the Nonlinear Schrödinger Equation in 1D with a generic trapping potential with a single eigenvalue Cuccagna, Scipio Maeda, Masaya Analysis of PDEs We prove in dimension $d=1$ a result similar to Soffer and Weinstein Jour. Diff. Eq. 98 (1992) capturing for pure power nonlinearities the whole range of exponents $p>1$. The proof is based on the virial inequality of Kowalczyk \textit{et al.} J. Eur. Math. Soc. (JEMS) 24 (2022) with smoothing estimates like in Mizumachi J. Math. Kyoto Univ. 48 (2008). |
| title | On small energy solutions of the Nonlinear Schrödinger Equation in 1D with a generic trapping potential with a single eigenvalue |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.20191 |