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September/October 2011 A new proof of long-range scattering for critical nonlinear Schrödinger equations
Jun Kato, Fabio Pusateri
Differential Integral Equations 24(9/10): 923-940 (September/October 2011).

Abstract

We present a new proof of global existence and long range scattering, from small initial data, for the one--dimensional cubic gauge invariant nonlinear Schrödinger equation, and for Hartree equations in dimension $n \geq 2$. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi, and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.

Citation

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Jun Kato. Fabio Pusateri. "A new proof of long-range scattering for critical nonlinear Schrödinger equations." Differential Integral Equations 24 (9/10) 923 - 940, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35307
MathSciNet: MR2850346

Subjects:
Primary: 35Q55

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.24 • No. 9/10 • September/October 2011
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