The generalized fractional Benjamin-Bona-Mahony equation: Analytical and numerical results

Oruç G., Borluk H., Muslu G. M.

PHYSICA D-NONLINEAR PHENOMENA, cilt.409, 2020 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 409
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.physd.2020.132499
  • Dergi Adı: PHYSICA D-NONLINEAR PHENOMENA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

The generalized fractional Benjamin-Bona-Mahony (gfBBM) equation models the propagation of small amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. The equation involves two fractional terms unlike the well-known fBBM equation. In this paper, we prove local existence and uniqueness of the solutions for the Cauchy problem by using energy method. The sufficient conditions for the existence of solitary wave solutions are obtained. The Petviashvili method is proposed for the generation of the solitary wave solutions and their evolution in time is investigated numerically by Fourier spectral method. The efficiency of the numerical methods is tested and the relation between nonlinearity and fractional dispersion is observed by various numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.