Mathematical Research Letters

Volume 24 (2017)

Number 3

Scattering-like phenomena of the periodic defocusing NLS equation

Pages: 803 – 826



T. Kappeler (Department of Mathematics, University of Zürich, Switzerland)

B. Schaad (University of Kansas, Lawrence, Ks., U.S.A.)

P. Topalov (Northeastern University, Boston, Massachusetts, U.S.A.)


In this paper we prove approximation properties of the solutions of the defocusing NLS equation on the circle by nearly linear flows. In addition we show that spatially periodic solutions of the defocusing NLS equation evolving in fractional Sobolev spaces $H^s$ with $s \geq 1$ remain bounded for all times.

Received 7 June 2015

Accepted 9 January 2016

Published 1 September 2017