Mathematical Research Letters
Volume 15 (2008)
On the wave operators for the critical nonlinear Schrödinger equation
Pages: 185 – 195
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.