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 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 ow and the corresponding Airy ow is 1-smoothing.
One smoothing property of the scattering map of the KDV on R / Maspero, Alberto; Schaad, Beat. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 36:3(2016), pp. 1493-1537. [10.3934/dcds.2016.36.1493]
One smoothing property of the scattering map of the KDV on R
Maspero, Alberto
;
2016-01-01
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 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 ow and the corresponding Airy ow is 1-smoothing.File in questo prodotto:
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