Abstract
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.
| Original language | English |
|---|---|
| Article number | 132499 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 409 |
| DOIs | |
| Publication status | Published - Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 Elsevier B.V.
Funding
The authors would like to express sincere gratitude to the reviewers and the editor for their constructive suggestions which helped to improve the quality of this paper. The last author would like to thank Dr. Jiao He for helpful and fruitful communication. Goksu Oruc was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the grant 2211 . The first and the last authors were supported by Research Fund of Istanbul Technical University Project Number: 42257 .
| Funders | Funder number |
|---|---|
| TUBITAK | 2211 |
| Türkiye Bilimsel ve Teknolojik Araştirma Kurumu | |
| Istanbul Teknik Üniversitesi | 42257 |
Keywords
- Conserved quantities
- Generalized fractional Benjamin–Bona–Mahony equation
- Local existence
- Petviashvili method
- Solitary waves