Mathematical Research Letters

Volume 15 (2008)

Number 1

On the wave operators for the critical nonlinear Schrödinger equation

Pages: 185 – 195

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n1.a15

Authors

Rémi Carles (Centre National de la Recherche Scientifique)

Tohru Ozawa (Hokkaido University)

Abstract

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.

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