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


Amaral S., BORLUK H., Muslu G. M. , Natali F., Oruç G.

STUDIES IN APPLIED MATHEMATICS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1111/sapm.12428
  • Title of Journal : STUDIES IN APPLIED MATHEMATICS
  • Keywords: BBM-type equations, existence and uniqueness of minimizers, orbital stability, Petviashvili's method, spectral stability, SOLITARY WAVES, SUFFICIENT CONDITIONS, ORBITAL STABILITY, TRAVELING-WAVES, CONVERGENCE, INSTABILITY, KDV

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.