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- W1669707212 abstract "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{rqrq} 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." @default.
- W1669707212 created "2016-06-24" @default.
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- W1669707212 date "2003-07-07" @default.
- W1669707212 modified "2023-09-27" @default.
- W1669707212 title "Stability of Solitons for the KdV equation in H^s, 0 <= s< 1" @default.
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