On the stability of solitary wave solutions for a generalized fractional Benjamin-Bona-Mahony equation

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

NONLINEARITY, vol.35, no.3, pp.1152-1169, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1088/1361-6544/ac4816
  • Journal Name: NONLINEARITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1152-1169
  • Keywords: generalized fractional Benjamin-Bona-Mahony equation, orbital stability, spectral instability, solitary waves, CAMASSA-HOLM EQUATIONS, DISPERSIVE PERTURBATIONS, ORBITAL STABILITY, MODEL-EQUATIONS, GROUND-STATES, INSTABILITY, SOLITONS, DERIVATION, BURGERS, KDV
  • Istanbul Technical University Affiliated: Yes


In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well known smooth and positive solitary wave with large wave speed, we present the existence of smooth negative solitary waves having small wave speed. The spectral stability is then determined by analysing the behaviour of the associated linearized operator around the wave restricted to the orthogonal of the tangent space related to the momentum at the solitary wave. Since the analytical solution is not known, we generate the negative solitary waves numerically by using Petviashvili method. We also present some numerical experiments to observe the stability properties of solitary waves for various values of the order of nonlinearity and fractional derivative. Some remarks concerning the orbital stability are also celebrated.