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

^*Corresponding author for this work

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

40 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	397-410
Number of pages	14
Journal	Reviews in Mathematical Physics
Volume	9
Issue number	3
DOIs	https://doi.org/10.1142/S0129055X97000154
Publication status	Published - 1997 Apr
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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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",

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doi = "10.1142/S0129055X97000154",

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AU - Ozawa, T.

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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.

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JF - Reviews in Mathematical Physics

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

Abstract

ASJC Scopus subject areas

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