Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2015-06-05
Publication Place
-
Elsevier
Subject
Camassa–Holm equation, Fractional Camassa–Holm equation, Nonlocal elasticity, Improved Boussinesq equation, Asymptotic expansions
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0375-9601
Record ID
787d34b0-d310-48e1-a990-348e53bdd96c
Library Location
Natural and Mathematical Sciences
Date
2015-06-05
Sample Text
In this paper we provide a formal derivation of both the Camassa–Holm equation and the fractional Camassa–Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium. We first show that the equation of motion for the nonlocally and nonlinearly elastic medium reduces to the improved. Boussinesq equation for a particular choice of the kernel function appearing in the integral-type constitutive relation. We then derive the Camassa–Holm equation from the improved Boussinesq equation using an asymptotic expansion valid as nonlinearity and dispersion parameters that tend to zero independently. Our approach follows mainly the standard techniques used widely in the literature to derive the Camassa–Holm equation for shallow-water waves. The case where the Fourier transform of the kernel function has fractional powers is also considered and the fractional Camassa–Holm equation is derived using the asymptotic expansion technique.
DOI
10.1016/j.physleta.2015.01.031
Cilt
379
