On the existence, uniqueness and stability of Periodic Waves for the\n fractional Benjamin-Bona-Mahony equation

2021/04/01 by Sabrina Amaral, Amaral, Sabrina, Handan Borluk +7 · 1 citation
Mathematics · Physics and Astronomy · #35Q51 #35Q53 #76B25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2104.00400

openalex publication_date 2021/04/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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

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