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

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.

References in corpus (2)

• Inverse scattering for Schrödinger operators with Miura potentials, I. Unique Riccati representatives and ZS-AKNS systems
• Asymptotics of spectral quantities of Schrödinger operators

Cited by in corpus (2)

• KdV equation beyond standard assumptions on initial data
• Tame majorant analyticity for the Birkhoff map of the defocusing Nonlinear Schrödinger equation on the circle