Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Gabriel E. Bittencourt Moraes; Handan Borluk; Guilherme de Loreno; Gulcin M. Muslu; Fábio Natali

doi:10.1016/j.jde.2022.09.015

Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Gabriel E. Bittencourt Moraes, Handan Borluk, Guilherme de Loreno, Gulcin M. Muslu, Fábio Natali^*

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Araştırma sonucu: ???type-name??? › Makale › bilirkişi

4 Atıf (Scopus)

Özet

In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schrödinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	263-291
Sayfa sayısı	29
Dergi	Journal of Differential Equations
Hacim	341
DOI'lar	https://doi.org/10.1016/j.jde.2022.09.015
Yayın durumu	Yayınlandı - 25 Ara 2022

Bibliyografik not

Publisher Copyright:
© 2022 Elsevier Inc.

Finansman

G. de Loreno and G.E.B. Moraes are supported by the regular doctorate scholarship from CAPES/Brazil. F. Natali is partially supported by Fundação Araucária /Brazil (grant 002/2017 ), CNPq /Brazil (grant 303907/2021-5 ) and CAPES MathAmSud (grant 88881.520205/2020-01 ).

Finansörler	Finansör numarası
CAPES MathAmSud	88881.520205/2020-01
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Conselho Nacional de Desenvolvimento Científico e Tecnológico	303907/2021-5
Fundação Araucária	002/2017

Belgeye Erişim

10.1016/j.jde.2022.09.015

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

@article{c0a3d45531d04133be277484daa2644b,

title = "Orbital stability of periodic standing waves for the cubic fractional nonlinear Schr{\"o}dinger equation",

abstract = "In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schr{\"o}dinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schr{\"o}dinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.",

keywords = "Existence and uniqueness of minimizers, Fractional Schr{\"o}dinger equation, Orbital stability, Small-amplitude periodic waves",

author = "{Bittencourt Moraes}, {Gabriel E.} and Handan Borluk and {de Loreno}, Guilherme and Muslu, {Gulcin M.} and F{\'a}bio Natali",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = dec,

day = "25",

doi = "10.1016/j.jde.2022.09.015",

language = "English",

volume = "341",

pages = "263--291",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

AU - Bittencourt Moraes, Gabriel E.

AU - Borluk, Handan

AU - de Loreno, Guilherme

AU - Muslu, Gulcin M.

AU - Natali, Fábio

PY - 2022/12/25

Y1 - 2022/12/25

N2 - In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schrödinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.

AB - In this paper, the existence and orbital stability of the periodic standing wave solutions for the nonlinear fractional Schrödinger (fNLS) equation with cubic nonlinearity is studied. The existence is determined by using a minimizing constrained problem in the complex setting and it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding the oscillation theorem for fractional Hill operators and the Vakhitov-Kolokolov condition, well known for Schrödinger equations. We then perform a numerical approach to generate the periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.

KW - Existence and uniqueness of minimizers

KW - Fractional Schrödinger equation

KW - Orbital stability

KW - Small-amplitude periodic waves

UR - http://www.scopus.com/inward/record.url?scp=85138500911&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2022.09.015

DO - 10.1016/j.jde.2022.09.015

M3 - Article

AN - SCOPUS:85138500911

SN - 0022-0396

VL - 341

SP - 263

EP - 291

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

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