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

J. Ginibre; T. Ozawa

doi:10.1007/BF02097031

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

J. Ginibre^*, T. Ozawa

^*この研究の対応する著者

研究成果: Article › 査読

141 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	619-645
ページ数	27
ジャーナル	Communications in Mathematical Physics
巻	151
号	3
DOI	https://doi.org/10.1007/BF02097031
出版ステータス	Published - 1993 2月
外部発表	はい

ASJC Scopus subject areas

統計物理学および非線形物理学
数理物理学

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10.1007/BF02097031

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abstract = "We consider the scattering problem for the non-linear Schr{\"o}dinger (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.",

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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.

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

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