### 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.

Original language | English |
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Pages (from-to) | 185-195 |

Number of pages | 11 |

Journal | Mathematical Research Letters |

Volume | 15 |

Issue number | 1 |

Publication status | Published - 2008 Jan |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*15*(1), 185-195.

**On the wave operators for the critical nonlinear Schrödinger equation.** / Carles, Rémi; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 15, no. 1, pp. 185-195.

}

TY - JOUR

T1 - On the wave operators for the critical nonlinear Schrödinger equation

AU - Carles, Rémi

AU - Ozawa, Tohru

PY - 2008/1

Y1 - 2008/1

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.

UR - http://www.scopus.com/inward/record.url?scp=41149125148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41149125148&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:41149125148

VL - 15

SP - 185

EP - 195

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 1

ER -