Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2015
Publication Place
-
Estonian Academy of Sciences
Subject
nonlocal elasticity, Korteweg–de Vries equation, Benjamin–Bona–Mahony equation, Camassa–Holm equation, fractional Camassa–Holm equation
Type
Document
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
2-s2.0-84947804639
Record ID
1fd9d3c8-37f8-4bc7-9cfb-b6854cfaa518
Library Location
Natural and Mathematical Sciences
Date
2015
Sample Text
We consider unidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral with a suitable kernel function. We first give a brief review of asymptotic wave models describing the unidirectional propagation of small-but-finite amplitude long waves. When the kernel function is the well-known exponential kernel, the asymptotic description is provided by the Korteweg–de Vries (KdV) equation, the Benjamin–Bona–Mahony (BBM) equation, or the Camassa–Holm (CH) equation. When the Fourier transform of the kernel function has fractional powers, it turns out that fractional forms of these equations describe unidirectional propagation of the waves. We then compare the exact solutions of the KdV equation and the BBM equation with the numerical solutions of the nonlocal model. We observe that the solution of the nonlocal model is well approximated by associated solutions of the KdV equation and the BBM equation over the time interval considered.
DOI
10.3176/proc.2015.3.08
Cilt
64
