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arXiv · 1412.3268

One smoothing property of the scattering map of the KdV on $\mathbb R$

Alberto Maspero·Beat Schaad
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Abstract

In this paper we prove that in appropriate weighted Sobolev spaces, in the case of no bound states, the scattering map of the Korteweg-de Vries (KdV) on $\mathbb R$ is a perturbation of the Fourier transform by a regularizing operator. As an application of this result, we show that the difference of the KdV flow and the corresponding Airy flow is 1-smoothing.

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Alberto Maspero, Beat Schaad. 2014-12-10. One smoothing property of the scattering map of the KdV on $\mathbb R$. https://doi.org/10.3934/dcds.2016.36.1493

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