The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916419783884800 |
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| author | Cuccagna, Scipio Maeda, Masaya |
| author_facet | Cuccagna, Scipio Maeda, Masaya |
| contents | For exponents $p$ satisfying $0<|p-3|\ll 1$ and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable. The proof is similar to a related result of Martel, preprint arXiv:2312.11016, for a cubic quintic NLS. Here we modify the second part of Martel's argument, replacing the second virial inequality for a transformed problem with a smoothing estimate on the initial problem, appropriately tamed by multiplying the initial variables and equations by a cutoff. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$ Cuccagna, Scipio Maeda, Masaya Analysis of PDEs 35Q55 For exponents $p$ satisfying $0<|p-3|\ll 1$ and only in the context of spatially even solutions we prove that the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable. The proof is similar to a related result of Martel, preprint arXiv:2312.11016, for a cubic quintic NLS. Here we modify the second part of Martel's argument, replacing the second virial inequality for a transformed problem with a smoothing estimate on the initial problem, appropriately tamed by multiplying the initial variables and equations by a cutoff. |
| title | The asymptotic stability on the line of ground states of the pure power NLS with $0<|p-3|\ll 1$ |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2404.14287 |