On the wave operators for the critical nonlinear Schrodinger equation

Rémi Carles (1, 2) , Tohru Ozawa (3)

1 ICP - Institut CNRS-PAULI
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 Department of Mathematics, Hokkaido University

We prove that for the mass critical nonlinear Schrodinger 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 mass critical nonlinear Schrodinger equation and a nonlinear Schrodinger equation of derivative type.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rémi Carles, Tohru Ozawa. On the wave operators for the critical nonlinear Schrodinger equation. Mathematical Research Letters, 2008, 15 (1), pp.185-195. ⟨10.4310/MRL.2008.v15.n1.a15⟩. ⟨hal-00133041⟩