On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

Sabrina Amaral; Handan Borluk; Gulcin M. Muslu; Fábio Natali; Goksu Oruc

doi:10.1111/sapm.12428

On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

Sabrina Amaral, Handan Borluk, Gulcin M. Muslu, Fábio Natali^*, Goksu Oruc

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

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

7 Atıf (Scopus)

Özet

The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin–Bona–Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	62-98
Sayfa sayısı	37
Dergi	Studies in Applied Mathematics
Hacim	148
Basın numarası	1
DOI'lar	https://doi.org/10.1111/sapm.12428
Yayın durumu	Yayınlandı - Oca 2022

Bibliyografik not

Publisher Copyright:
© 2021 Wiley Periodicals LLC

Finansman

The authors are grateful to the two anonymous referees for their valuable suggestions and comments which greatly improved the presentation of the paper. S. Amaral was supported by the regular doctorate scholarship from CAPES. F. Natali is partially supported by CNPq (grant 304240/2018‐4), Fundação Araucária (grant 002/2017), 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	002/2017, 304240/2018‐4
Fundação Araucária

Belgeye Erişim

10.1111/sapm.12428

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation",

abstract = "The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin–Bona–Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.",

author = "Sabrina Amaral and Handan Borluk and Muslu, {Gulcin M.} and F{\'a}bio Natali and Goksu Oruc",

note = "Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC",

year = "2022",

month = jan,

doi = "10.1111/sapm.12428",

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volume = "148",

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TY - JOUR

T1 - On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

AU - Amaral, Sabrina

AU - Borluk, Handan

AU - Muslu, Gulcin M.

AU - Natali, Fábio

AU - Oruc, Goksu

PY - 2022/1

Y1 - 2022/1

N2 - The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin–Bona–Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.

AB - The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result for the single-lobe solution obtained by a constrained minimization problem. The spectral stability is then shown by determining that the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum and mass at the periodic wave has no negative eigenvalues. We propose the Petviashvili's method to investigate the spectral stability of the periodic waves for the fractional Benjamin–Bona–Mahony equation, numerically. Some remarks concerning the orbital stability of periodic traveling waves are also presented.

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U2 - 10.1111/sapm.12428

DO - 10.1111/sapm.12428

M3 - Article

AN - SCOPUS:85111480054

SN - 0022-2526

VL - 148

SP - 62

EP - 98

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

IS - 1

ER -

On the existence, uniqueness, and stability of periodic waves for the fractional Benjamin–Bona–Mahony equation

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap