On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908709939052544 |
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| author | Cuccagna, Scipio Maeda, Masaya |
| author_facet | Cuccagna, Scipio Maeda, Masaya |
| contents | We apply our idea, which previously we used in the analysis of the pure power NLS, consisting in spitting the virial inequality method into a large energy inequality combined with Kato smoothing, to the case of generalized Korteweg--De Vries pure power equations. We assume that a solution remains for all positive times very close to a soliton and then we prove an asymptotic stability result for $t\to +\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$ Cuccagna, Scipio Maeda, Masaya Analysis of PDEs We apply our idea, which previously we used in the analysis of the pure power NLS, consisting in spitting the virial inequality method into a large energy inequality combined with Kato smoothing, to the case of generalized Korteweg--De Vries pure power equations. We assume that a solution remains for all positive times very close to a soliton and then we prove an asymptotic stability result for $t\to +\infty$. |
| title | On stabilization at a soliton for generalized Korteweg--De Vries pure power equation for any power $p\in (1,5)$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.05579 |