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Small data scattering
and soliton stability in $\dot{H}^{-1/6}$ for the quartic KdV
equation
Herbert Koch and Jeremy L. Marzuola |
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Vol. 5 (2012), No. 1, 145–198
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Abstract |
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We prove scattering for perturbations of solitons in the scaling space appropriate for the quartic nonlinearity, namely . The article relies strongly on refined estimates for a KdV equation linearized at the soliton. In contrast to the work of Tao, we are able to work purely in the scaling space without additional regularity assumptions, allowing us to construct wave operators and a weak version of inverse wave operators. |
Keywords
Korteweg–de-Vries, solitons, scattering
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Mathematical Subject Classification 2000
Primary: 35K40, 35Q51, 35Q53
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Milestones
Received: 1 February 2010
Revised: 11 August 2010
Accepted: 1 October 2010
Published: 25 June 2012
Proposed: Frank Merle
Seconded: Gilles Lebeau, Terence Tao
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Authors |
| Herbert Koch | |
| Mathematisches Institut Universität Bonn Endenicher Allee 60 D-53115 Bonn Germany |
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| Jeremy L. Marzuola | |
| Department of Mathematics University of North Carolina Chapel Hill, NC 27599 United States |
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