Author
Oruc, G., Borluk, Handan, Muslu, G. M.
Publication Date
2020-08
Publication Place
-
Elsevier
Subject
Generalized fractional Benjamin–Bona–Mahony equation, Conserved quantities, Local existence, Solitary waves, Petviashvili method
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0167-2789
Record ID
55582a8b-872c-49cb-974d-cc4d392843ed
Library Location
Natural and Mathematical Sciences
Date
2020-08
Notes
TÜBİTAK ; Istanbul Technical University
Sample Text
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.
DOI
10.1016/j.physd.2020.132499
Cilt
409
