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, cilt.148, sa.1, ss.62-98, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 148 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1111/sapm.12428
  • Dergi Adı: STUDIES IN APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Applied Science & Technology Source, Business Source Elite, Business Source Premier, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.62-98
  • Anahtar Kelimeler: 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
  • İstanbul Teknik Üniversitesi Adresli: Evet

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.