# American Institute of Mathematical Sciences

September  2003, 2(3): 277-296. doi: 10.3934/cpaa.2003.2.277

## Low regularity stability of solitons for the KDV equation

 1 Massachusetts Institute of Technology, United States, United States

Received  January 2003 Revised  April 2003 Published  June 2003

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 results of [7] for the nonlinear Schrödinger equation, and obtains the same maximal growth rate in $t$. Our argument is based on the "I-method" used in [7] and other papers of Colliander, Keel, Staffilani, Takaoka and Tao.
Citation: S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 277-296. doi: 10.3934/cpaa.2003.2.277
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