Stability of Solitons for the KdV equation in H^s, 0 <= s< 1

dc.creatorRaynor, S.
dc.creatorStaffilani, G.
dc.date2003-07-07
dc.date.accessioned2026-07-07T04:59:28Z
dc.date.available2026-07-07T04:59:28Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/math/0307084
dc.identifierhttp://arxiv.org/abs/math/0307084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67995
dc.subjectAnalysis of PDEs
dc.subject35Q53, 42B35, 37K10, 37B25
dc.titleStability of Solitons for the KdV equation in H^s, 0 <= s< 1
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