Erbay, Hüsnü Ata and Erbay, Saadet and Erkip, Albert (2015) Derivation of the CamassaHolm equations for elastic waves. Physics Letters A, 379 (1213). pp. 956961. ISSN 03759601 (Print) 18732429 (Online)
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Official URL: http://dx.doi.org/10.1016/j.physleta.2015.01.031
Abstract
In this paper we provide a formal derivation of both the CamassaHolm equation and the fractional CamassaHolm equation for the propagation of smallbutfinite 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 integraltype constitutive relation. We then derive the CamassaHolm 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 CamassaHolm equation for shallowwater waves. The case where the Fourier transform of the kernel function has fractional powers is also considered and the fractional CamassaHolm equation is derived using the asymptotic expansion technique.
Item Type:  Article 

Uncontrolled Keywords:  CamassaHolm equation; Fractional CamassaHolm equation; Nonlocal elasticity; Improved Boussinesq equation; Asymptotic expansions 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Albert Erkip 
Date Deposited:  08 Dec 2015 14:45 
Last Modified:  23 Aug 2019 10:25 
URI:  https://research.sabanciuniv.edu/id/eprint/27409 
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Derivation of the CamassaHolm equations for elastic waves. (deposited 02 Feb 2015 16:06)
 Derivation of the CamassaHolm equations for elastic waves. (deposited 08 Dec 2015 14:45) [Currently Displayed]