Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

Jean Claude Saut; Jun Ichi Segata

doi:10.3934/dcds.2019009

Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

Jean Claude Saut, Jun Ichi Segata

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

4 Citations (Scopus)

Abstract

We consider the asymptotic behavior in time of solutions to the nonlinear Schrödinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as t → ∞.

Original language	English
Pages (from-to)	219-239
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	39
Issue number	1
DOIs	https://doi.org/10.3934/dcds.2019009
Publication status	Published - Jan 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcds.2019009

Fingerprint Dive into the research topics of 'Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion'. Together they form a unique fingerprint.

Cite this

@article{def2c374c6814d149d70dcaca27672fb,

title = "Asymptotic behavior in time of solution to the nonlinear Schr{\"o}dinger equation with higher order anisotropic dispersion",

abstract = "We consider the asymptotic behavior in time of solutions to the nonlinear Schr{\"o}dinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as t → ∞.",

author = "Saut, {Jean Claude} and Segata, {Jun Ichi}",

note = "Funding Information: Acknowledgments. We thank the referee for careful reading of the manuscript and for fruitful suggestions. The part of this work was done while J.S was visiting at Department of Mathematics at Universit{\'e}de Paris-Sud, Orsay whose hospitality they gratefully acknowledge. J.S. is partially supported by JSPS, Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation, Grant-in-Aid for Young Scientists (A) 25707004, and Grant-in-Aid for Scientific Research (B) 17H02851.",

year = "2019",

month = jan,

doi = "10.3934/dcds.2019009",

language = "English",

volume = "39",

pages = "219--239",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "1",

}

TY - JOUR

T1 - Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

AU - Saut, Jean Claude

AU - Segata, Jun Ichi

N1 - Funding Information: Acknowledgments. We thank the referee for careful reading of the manuscript and for fruitful suggestions. The part of this work was done while J.S was visiting at Department of Mathematics at Universitéde Paris-Sud, Orsay whose hospitality they gratefully acknowledge. J.S. is partially supported by JSPS, Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation, Grant-in-Aid for Young Scientists (A) 25707004, and Grant-in-Aid for Scientific Research (B) 17H02851.

PY - 2019/1

Y1 - 2019/1

N2 - We consider the asymptotic behavior in time of solutions to the nonlinear Schrödinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as t → ∞.

AB - We consider the asymptotic behavior in time of solutions to the nonlinear Schrödinger equation with fourth order anisotropic dispersion (4NLS) which describes the propagation of ultrashort laser pulses in a medium with anomalous time-dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to (4NLS) which scatters to a solution of the linearized equation of (4NLS) as t → ∞.

UR - http://www.scopus.com/inward/record.url?scp=85056112672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056112672&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019009

DO - 10.3934/dcds.2019009

M3 - Article

AN - SCOPUS:85056112672

VL - 39

SP - 219

EP - 239

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 1

ER -