### Abstract

We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|^{-1} in space dimension n≥2. We prove the existence of modified wave operators in the L^{2} sense on a dense set of small and sufficiently regular asymptotic states.

Original language | English |
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Pages (from-to) | 619-645 |

Number of pages | 27 |

Journal | Communications in Mathematical Physics |

Volume | 151 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1993 Feb |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2.** / Ginibre, J.; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 151, no. 3, pp. 619-645. https://doi.org/10.1007/BF02097031

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TY - JOUR

T1 - Long range scattering for non-linear Schrödinger and Hartree equations in space dimension n≥2

AU - Ginibre, J.

AU - Ozawa, Tohru

PY - 1993/2

Y1 - 1993/2

N2 - We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|-1 in space dimension n≥2. We prove the existence of modified wave operators in the L2 sense on a dense set of small and sufficiently regular asymptotic states.

AB - We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical power p=1+2/n in space dimensions n=2 and 3 and for the Hartree equation with potential |x|-1 in space dimension n≥2. We prove the existence of modified wave operators in the L2 sense on a dense set of small and sufficiently regular asymptotic states.

UR - http://www.scopus.com/inward/record.url?scp=0001632973&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001632973&partnerID=8YFLogxK

U2 - 10.1007/BF02097031

DO - 10.1007/BF02097031

M3 - Article

VL - 151

SP - 619

EP - 645

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -