Stability of Solitons for the KdV equation in H^s, 0 <= s< 1
| dc.creator | Raynor, S. | |
| dc.creator | Staffilani, G. | |
| dc.date | 2003-07-07 | |
| dc.date.accessioned | 2026-07-07T04:59:28Z | |
| dc.date.available | 2026-07-07T04:59:28Z | |
| dc.description | We study the long-time stability of soliton solutions to the Korteweg-deVries equation. We consider solutions $u$ to the KdV with initial data in $H^s$, $0 \leq s < 1$, that are initially close in $H^s$ norm to a soliton. We prove that the possible orbital instability of these ground states is at most polynomial in time. This is an analogue to the $H^s$ orbital instability result of \cite{CKSTT3}, and obtains the same maximal growth rate in $t$. Our argument is based on the {``}$I$-method{\rq\rq} used in \cite{CKSTT3} and other papers of Colliander, Keel, Staffilani, Takaoka and Tao, which pushes these $H^s$ functions to the $H^1$ norm. | |
| dc.identifier | https://arxiv.org/abs/math/0307084 | |
| dc.identifier | http://arxiv.org/abs/math/0307084 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67995 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53, 42B35, 37K10, 37B25 | |
| dc.title | Stability of Solitons for the KdV equation in H^s, 0 <= s< 1 | |
| dc.type | text |