## Derivation of the Camassa-Holm equations for elastic waves
Erbay, Hüsnü Ata and Erbay, Saadet and Erkip, Albert (2015)
Full text not available from this repository. Official URL: http://dx.doi.org/10.1016/j.physleta.2015.01.031 ## AbstractIn 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.
## Available Versions of this Item- Derivation of the Camassa-Holm equations for elastic waves. (deposited 02 Feb 2015 16:06)
- Derivation of the Camassa-Holm equations for elastic waves. (deposited 08 Dec 2015 14:45)
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- Derivation of the Camassa-Holm equations for elastic waves. (deposited 08 Dec 2015 14:45)
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