Scattering-like phenomena of the periodic defocusing NLS equation

Abstract

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 solutions of the defocusing NLS equation evolving in fractional Sobolev spaces $H^s$ with $s\ge 1$ remain bounded for all times.

References in corpus (1)

• Asymptotics of spectral quantities of Zakharov-Shabat operators