Long range scattering for nonlinear Schrödinger equations in one space dimension

Research output: Contribution to journalArticle

144 Citations (Scopus)

Abstract

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

Original languageEnglish
Pages (from-to)479-493
Number of pages15
JournalCommunications in Mathematical Physics
Volume139
Issue number3
DOIs
Publication statusPublished - 1991 Aug
Externally publishedYes

Fingerprint

Wave Operator
nonlinear equations
Nonlinear Equations
Scattering
Sobolev space
operators
Lebesgue Space
Scattering Problems
scattering
Range of data
Sobolev Spaces
Figure
nonlinearity
Nonlinearity
Zero

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Long range scattering for nonlinear Schrödinger equations in one space dimension. / Ozawa, Tohru.

In: Communications in Mathematical Physics, Vol. 139, No. 3, 08.1991, p. 479-493.

Research output: Contribution to journalArticle

@article{90e0b25df2954e1ba670941661dee3ab,
title = "Long range scattering for nonlinear Schr{\"o}dinger equations in one space dimension",
abstract = "We consider the scattering problem for the nonlinear Schr{\"o}dinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.",
author = "Tohru Ozawa",
year = "1991",
month = "8",
doi = "10.1007/BF02101876",
language = "English",
volume = "139",
pages = "479--493",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Long range scattering for nonlinear Schrödinger equations in one space dimension

AU - Ozawa, Tohru

PY - 1991/8

Y1 - 1991/8

N2 - We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

AB - We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions:[Figure not available: see fulltext.] where ∂ = ∂/∂x, λ∈R{set minus}{0}, μ∈R, p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue space L2(R) or in the Sobolev space H1(R)., The modified wave operators are introduced in order to control the long range nonlinearity λ|u|2u.

UR - http://www.scopus.com/inward/record.url?scp=0001366166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001366166&partnerID=8YFLogxK

U2 - 10.1007/BF02101876

DO - 10.1007/BF02101876

M3 - Article

VL - 139

SP - 479

EP - 493

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -