Vol. 5, No. 1, 2012

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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

Vol. 5 (2012), No. 1, 145–198

We prove scattering for perturbations of solitons in the scaling space appropriate for the quartic nonlinearity, namely 16. 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.

Korteweg–de-Vries, solitons, scattering
Mathematical Subject Classification 2000
Primary: 35K40, 35Q51, 35Q53
Received: 1 February 2010
Revised: 11 August 2010
Accepted: 1 October 2010
Published: 25 June 2012

Proposed: Frank Merle
Seconded: Gilles Lebeau, Terence Tao
Herbert Koch
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D-53115 Bonn
Jeremy L. Marzuola
Department of Mathematics
University of North Carolina
Chapel Hill, NC 27599
United States