Modified wave operators for nonlinear Schrödinger equations in one and two dimensions

Nakao Hayashi; Pavel I. Naumkin; Akihiro Shimomura; Satoshi Tonegawa

Modified wave operators for nonlinear Schrödinger equations in one and two dimensions

Nakao Hayashi, Pavel I. Naumkin, Akihiro Shimomura, Satoshi Tonegawa

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

Abstract

We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Electronic Journal of Differential Equations
Volume	2004
Publication status	Published - 2004 Apr 21
Externally published	Yes

Keywords

Modified wave operators
Nonlinear Schrödinger equations

ASJC Scopus subject areas

Analysis

Cite this

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abstract = "We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr{\"o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].",

keywords = "Modified wave operators, Nonlinear Schr{\"o}dinger equations",

author = "Nakao Hayashi and Naumkin, {Pavel I.} and Akihiro Shimomura and Satoshi Tonegawa",

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AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

AU - Shimomura, Akihiro

AU - Tonegawa, Satoshi

PY - 2004/4/21

Y1 - 2004/4/21

N2 - We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].

AB - We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].

KW - Modified wave operators

KW - Nonlinear Schrödinger equations

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JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Modified wave operators for nonlinear Schrödinger equations in one and two dimensions

Abstract

Keywords

ASJC Scopus subject areas

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