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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