Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Kei Nakamura; Tohru Ozawa

doi:10.3934/dcds.2013.33.789

Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Kei Nakamura^*, Tohru Ozawa

^*Corresponding author for this work

School of Advanced Science and Engineering

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

1 Citation (Scopus)

Abstract

We study the Cauchy problem for cubic Schrödinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L ²(R) without any approximating arguments.

Original language	English
Pages (from-to)	789-801
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2013.33.789
Publication status	Published - 2013

Keywords

Blow-up
Nonlinear Schrödinger equations
Scattering.

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2013.33.789

Cite this

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title = "Finite charge solutions to cubic schr{\"o}dinger equations with a nonlocal nonlinearity in one space dimension",

abstract = "We study the Cauchy problem for cubic Schr{\"o}dinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.",

keywords = "Blow-up, Nonlinear Schr{\"o}dinger equations, Scattering.",

author = "Kei Nakamura and Tohru Ozawa",

year = "2013",

doi = "10.3934/dcds.2013.33.789",

language = "English",

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issn = "1078-0947",

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AU - Nakamura, Kei

AU - Ozawa, Tohru

PY - 2013

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N2 - We study the Cauchy problem for cubic Schrödinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.

AB - We study the Cauchy problem for cubic Schrödinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.

KW - Blow-up

KW - Nonlinear Schrödinger equations

KW - Scattering.

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 2

ER -

Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Abstract

Keywords

ASJC Scopus subject areas

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