Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

Kazuki Aoki; Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00030-016-0420-z

Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

Kazuki Aoki, Nakao Hayashi, Pavel I. Naumkin

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

7 Citations (Scopus)

Abstract

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation [Equation not available: see fulltext.]where n= 1 , 2. We prove global existence of small solutions under the growth condition of f(u) satisfying |∂ujf(u)|≤C|u|p-j, where p>1+4n,0≤j≤3.

Original language	English
Article number	65
Journal	Nonlinear Differential Equations and Applications
Volume	23
Issue number	6
DOIs	https://doi.org/10.1007/s00030-016-0420-z
Publication status	Published - 2016 Dec 1
Externally published	Yes

Keywords

Fourth-order nonlinear Schrödinger equation
Global existence
Non gauge invariant

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-016-0420-z

Cite this

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title = "Global existence of small solutions for the fourth-order nonlinear Schr{\"o}dinger equation",

abstract = "We consider the Cauchy problem for the fourth-order nonlinear Schr{\"o}dinger equation [Equation not available: see fulltext.]where n= 1 , 2. We prove global existence of small solutions under the growth condition of f(u) satisfying |∂ujf(u)|≤C|u|p-j, where p>1+4n,0≤j≤3.",

keywords = "Fourth-order nonlinear Schr{\"o}dinger equation, Global existence, Non gauge invariant",

author = "Kazuki Aoki and Nakao Hayashi and Naumkin, {Pavel I.}",

note = "Funding Information: We would like to thank the referee for useful comments on the scattering problem. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP25220702, JP15H03630. The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100616. Publisher Copyright: {\textcopyright} 2016, Springer International Publishing.",

year = "2016",

month = dec,

day = "1",

doi = "10.1007/s00030-016-0420-z",

language = "English",

volume = "23",

journal = "Nonlinear Differential Equations and Applications",

issn = "1021-9722",

publisher = "Birkhauser Verlag Basel",

number = "6",

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TY - JOUR

T1 - Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

AU - Aoki, Kazuki

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

N1 - Funding Information: We would like to thank the referee for useful comments on the scattering problem. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP25220702, JP15H03630. The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100616. Publisher Copyright: © 2016, Springer International Publishing.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation [Equation not available: see fulltext.]where n= 1 , 2. We prove global existence of small solutions under the growth condition of f(u) satisfying |∂ujf(u)|≤C|u|p-j, where p>1+4n,0≤j≤3.

AB - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation [Equation not available: see fulltext.]where n= 1 , 2. We prove global existence of small solutions under the growth condition of f(u) satisfying |∂ujf(u)|≤C|u|p-j, where p>1+4n,0≤j≤3.

KW - Fourth-order nonlinear Schrödinger equation

KW - Global existence

KW - Non gauge invariant

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U2 - 10.1007/s00030-016-0420-z

DO - 10.1007/s00030-016-0420-z

M3 - Article

AN - SCOPUS:84994805494

SN - 1021-9722

VL - 23

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 6

M1 - 65

ER -

Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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