On the wave operators for the critical nonlinear Schrödinger equation

Rémi Carles; Tohru Ozawa

doi:10.4310/MRL.2008.v15.n1.a15

On the wave operators for the critical nonlinear Schrödinger equation

Rémi Carles^*, Tohru Ozawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We prove that for the L²-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.

Original language	English
Pages (from-to)	185-195
Number of pages	11
Journal	Mathematical Research Letters
Volume	15
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2008.v15.n1.a15
Publication status	Published - 2008 Jan
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.4310/MRL.2008.v15.n1.a15

Cite this

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title = "On the wave operators for the critical nonlinear Schr{\"o}dinger equation",

abstract = "We prove that for the L2-critical nonlinear Schr{\"o}dinger 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{\"o}dinger equation and a nonlinear Schr{\"o}dinger equation of derivative type.",

author = "R{\'e}mi Carles and Tohru Ozawa",

year = "2008",

month = jan,

doi = "10.4310/MRL.2008.v15.n1.a15",

language = "English",

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journal = "Mathematical Research Letters",

issn = "1073-2780",

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AU - Carles, Rémi

AU - Ozawa, Tohru

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N2 - We prove that for the L2-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.

AB - We prove that for the L2-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.

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U2 - 10.4310/MRL.2008.v15.n1.a15

DO - 10.4310/MRL.2008.v15.n1.a15

M3 - Article

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VL - 15

SP - 185

EP - 195

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 1

ER -

On the wave operators for the critical nonlinear Schrödinger equation

Abstract

ASJC Scopus subject areas

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