Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

M. Nakamura; T. Ozawa

doi:10.1142/S0129055X97000154

Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

M. Nakamura, T. Ozawa

研究成果: Article › 査読

34 被引用数 (Scopus)

抄録

We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

本文言語	English
ページ（範囲）	397-410
ページ数	14
ジャーナル	Reviews in Mathematical Physics
巻	9
号	3
DOI	https://doi.org/10.1142/S0129055X97000154
出版ステータス	Published - 1997 4
外部発表	はい

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

文献へのアクセス

10.1142/S0129055X97000154

フィンガープリント「Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{af4f8fa4807d426791420d406f99ff87,

title = "Low energy scattering for nonlinear Schr{\"o}dinger equations in fractional order Sobolev spaces",

abstract = "We consider the scattering problem for the nonlinear Schr{\"o}dinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.",

author = "M. Nakamura and T. Ozawa",

year = "1997",

month = apr,

doi = "10.1142/S0129055X97000154",

language = "English",

volume = "9",

pages = "397--410",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces

AU - Nakamura, M.

AU - Ozawa, T.

PY - 1997/4

Y1 - 1997/4

N2 - We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

AB - We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s ≥ n/2-2/(p-1) ≥ 0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n ≥ 1.

UR - http://www.scopus.com/inward/record.url?scp=0031285644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031285644&partnerID=8YFLogxK

U2 - 10.1142/S0129055X97000154

DO - 10.1142/S0129055X97000154

M3 - Article

AN - SCOPUS:0031285644

VL - 9

SP - 397

EP - 410

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 3

ER -