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

^*Corresponding author for this work

Department of Mathematics Engineering

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

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	62-98
Number of pages	37
Journal	Studies in Applied Mathematics
Volume	148
Issue number	1
DOIs	https://doi.org/10.1111/sapm.12428
Publication status	Published - Jan 2022

Bibliographical note

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© 2021 Wiley Periodicals LLC

Funding

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).

Funders	Funder number
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

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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.",

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AU - Oruc, Goksu

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

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