Modified wave operators for nonlinear Schrödinger equations in lower order Sobolev spaces

Nakao Hayashi; Huimei Wang; Pavel I. Naumkin

doi:10.1142/S0219891611002561

Modified wave operators for nonlinear Schrödinger equations in lower order Sobolev spaces

Nakao Hayashi, Huimei Wang, Pavel I. Naumkin

Research Alliance Center for Mathematical Sciences (RACMaS)

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

8 Citations (Scopus)

Abstract

We study the final value problem for the nonlinear Schrödinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.

Original language	English
Pages (from-to)	759-775
Number of pages	17
Journal	Journal of Hyperbolic Differential Equations
Volume	8
Issue number	4
DOIs	https://doi.org/10.1142/S0219891611002561
Publication status	Published - 2011 Dec

Keywords

Modified wave operators
lower order Sobolev
nonlinear Schrödinger equations

ASJC Scopus subject areas

Analysis
Mathematics(all)

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10.1142/S0219891611002561

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title = "Modified wave operators for nonlinear Schr{\"o}dinger equations in lower order Sobolev spaces",

abstract = "We study the final value problem for the nonlinear Schr{\"o}dinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.",

keywords = "Modified wave operators, lower order Sobolev, nonlinear Schr{\"o}dinger equations",

author = "Nakao Hayashi and Huimei Wang and Naumkin, {Pavel I.}",

note = "Funding Information: The work of N. Hayashi was partially supported by KAKENHI (no. 19340030) and the work of P. I. Naumkin is partially supported by CONACYT and PAPIIT. We are grateful to an unknown referee for many useful suggestions and comments.",

year = "2011",

month = dec,

doi = "10.1142/S0219891611002561",

language = "English",

volume = "8",

pages = "759--775",

journal = "Journal of Hyperbolic Differential Equations",

issn = "0219-8916",

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

number = "4",

}

TY - JOUR

T1 - Modified wave operators for nonlinear Schrödinger equations in lower order Sobolev spaces

AU - Hayashi, Nakao

AU - Wang, Huimei

AU - Naumkin, Pavel I.

N1 - Funding Information: The work of N. Hayashi was partially supported by KAKENHI (no. 19340030) and the work of P. I. Naumkin is partially supported by CONACYT and PAPIIT. We are grateful to an unknown referee for many useful suggestions and comments.

PY - 2011/12

Y1 - 2011/12

N2 - We study the final value problem for the nonlinear Schrödinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.

AB - We study the final value problem for the nonlinear Schrödinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.

KW - Modified wave operators

KW - lower order Sobolev

KW - nonlinear Schrödinger equations

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DO - 10.1142/S0219891611002561

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SP - 759

EP - 775

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

SN - 0219-8916

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