Self-similar solutions to the derivative nonlinear Schrödinger equation

Kazumasa Fujiwara; Vladimir Georgiev; Tohru Ozawa

doi:10.1016/j.jde.2019.11.089

Self-similar solutions to the derivative nonlinear Schrödinger equation

Kazumasa Fujiwara^*, Vladimir Georgiev, Tohru Ozawa

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

A class of self-similar solutions to the derivative nonlinear Schrödinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

Original language	English
Pages (from-to)	7940-7961
Number of pages	22
Journal	Journal of Differential Equations
Volume	268
Issue number	12
DOIs	https://doi.org/10.1016/j.jde.2019.11.089
Publication status	Published - 2020 Jun 5

Keywords

Derivative nonlinear Schrödinger equations
Self-similar solution

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2019.11.089

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@article{a297417f290848aab5a4c8d0f5fd2d2b,

title = "Self-similar solutions to the derivative nonlinear Schr{\"o}dinger equation",

abstract = "A class of self-similar solutions to the derivative nonlinear Schr{\"o}dinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.",

keywords = "Derivative nonlinear Schr{\"o}dinger equations, Self-similar solution",

author = "Kazumasa Fujiwara and Vladimir Georgiev and Tohru Ozawa",

note = "Funding Information: The first author was supported in part by Grant-in-Aid for JSPS Fellows Number 201900334.The second author was supported in part by Project 2017 ?Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari? of INDAM, GNAMPA - Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2020",

month = jun,

day = "5",

doi = "10.1016/j.jde.2019.11.089",

language = "English",

volume = "268",

pages = "7940--7961",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "12",

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TY - JOUR

T1 - Self-similar solutions to the derivative nonlinear Schrödinger equation

AU - Fujiwara, Kazumasa

AU - Georgiev, Vladimir

AU - Ozawa, Tohru

N1 - Funding Information: The first author was supported in part by Grant-in-Aid for JSPS Fellows Number 201900334.The second author was supported in part by Project 2017 ?Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari? of INDAM, GNAMPA - Gruppo Nazionale per l'Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016. Publisher Copyright: © 2019 Elsevier Inc.

PY - 2020/6/5

Y1 - 2020/6/5

N2 - A class of self-similar solutions to the derivative nonlinear Schrödinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

AB - A class of self-similar solutions to the derivative nonlinear Schrödinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is obtained from the nonlinear interaction of profile functions. This is a remarkable difference from the pseudo-conformally invariant case, where the logarithmic correction comes from the linear part of the equations of the profile functions.

KW - Derivative nonlinear Schrödinger equations

KW - Self-similar solution

UR - http://www.scopus.com/inward/record.url?scp=85081654699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85081654699&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2019.11.089

DO - 10.1016/j.jde.2019.11.089

M3 - Article

AN - SCOPUS:85081654699

SN - 0022-0396

VL - 268

SP - 7940

EP - 7961

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 12

ER -

Self-similar solutions to the derivative nonlinear Schrödinger equation

Abstract

Keywords

ASJC Scopus subject areas

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