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
Abstract

We prove scattering for perturbations of solitons in the scaling space appropriate for the quartic nonlinearity, namely ${Ḣ}^{-1∕6}$. 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
Mathematical Subject Classification 2000
Primary: 35K40, 35Q51, 35Q53