Mathematical Research Letters

Volume 15 (2008)

Number 1

On the wave operators for the critical nonlinear Schrödinger equation

Pages: 185 – 195



Rémi Carles (Centre National de la Recherche Scientifique)

Tohru Ozawa (Hokkaido University)


We prove that for the $L^2$-critical nonlinear Schrödinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the one-dimensional case, we show a precise similarity between the $L^2$-critical nonlinear Schrödinger equation and a nonlinear Schrödinger equation of derivative type.

Published 1 January 2008