Mathematical Research Letters

Volume 15, Issue 1, January 2008 pp. 185-195.

On the wave operators for the critical nonlinear Schr\"odinger equation

Authors: Rémi Carles (1) and Tohru Ozawa (2)
Author institution: Centre National de la Recherche Scientifique (1) and Hokkaido University (2)

Summary: We prove that for the $L^2$-critical nonlinear Schr\"odinger 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 Schr\"odinger equation and a nonlinear Schr\"odinger equation of derivative type.

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