Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation

Jun Ichi Segata; Akihiro Shimomura

Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation

Jun Ichi Segata, Akihiro Shimomura

SCI - Mathematics

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

Abstract

We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.

Original language	English
Pages (from-to)	169-188
Number of pages	20
Journal	Communications in Applied Analysis
Volume	11
Issue number	2
Publication status	Published - 2007 Apr 1

ASJC Scopus subject areas

Analysis
Numerical Analysis
Modelling and Simulation
Applied Mathematics

Cite this

@article{b5f319d775974ae4b24a635661fc421e,

title = "Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schr{\"o}dinger type equation",

abstract = "We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schr{\"o}dinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.",

author = "Segata, {Jun Ichi} and Akihiro Shimomura",

year = "2007",

month = apr,

day = "1",

language = "English",

volume = "11",

pages = "169--188",

journal = "Communications in Applied Analysis",

issn = "1083-2564",

publisher = "Dynamic Publishers",

number = "2",

}

TY - JOUR

T1 - Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation

AU - Segata, Jun Ichi

AU - Shimomura, Akihiro

PY - 2007/4/1

Y1 - 2007/4/1

N2 - We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.

AB - We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.

UR - http://www.scopus.com/inward/record.url?scp=34347375488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34347375488&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34347375488

SN - 1083-2564

VL - 11

SP - 169

EP - 188

JO - Communications in Applied Analysis

JF - Communications in Applied Analysis

IS - 2

ER -

Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this