7 citations · 25 across the 6 of their papers we have counts for
4 papers · 1 filter
Scattering-like phenomena of the periodic defocusing NLS equation
T. Kappeler, B. Schaad, P. Topalov
In this paper we prove approximation properties of the solutions of the defoucsing NLS equation on the circle by nearly linear flows. In addition we show that spatially periodic so…
Semi-linearity of the non-linear Fourier transform of the defocusing NLS equation
T. Kappeler, B. Schaad, P. Topalov
In this paper we prove that the non-linear Fourier transform of the defocusing NLS equation on the circle is linear up to terms which are one order smoother.
One smoothing property of the scattering map of the KdV on
Alberto Maspero, Beat Schaad
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 is a perturbati…
Qualitative features of periodic solutions of KdV
T. Kappeler, B. Schaad, P. Topalov
In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\,…