Contents Online
Mathematical Research Letters
Volume 15 (2008)
Number 1
On the wave operators for the critical nonlinear Schrödinger equation
Pages: 185 – 195
DOI: https://dx.doi.org/10.4310/MRL.2008.v15.n1.a15
Authors
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.
Published 1 January 2008