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

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  • 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.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35P25, 37K15.

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