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

الأصل · EN

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 Hˢ, 0 ≤ s < 1, that are initially close in Hˢ 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 Hˢ orbital instability result of CKSTT3, and obtains the same maximal growth rate in t. Our argument is based on the ``I-method used in CKSTT3 and other papers of Colliander, Keel, Staffilani, Takaoka and Tao, which pushes these Hˢ functions to the H¹ norm.