Derivation of the Camassa-Holm equations for elastic waves

Name: Derivation of the Camassa-Holm equations for elastic waves
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Derivation of the Camassa-Holm equations for elastic waves
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2015-06-05
Basım Yeri	- Elsevier
Konu	Camassa–Holm equation, Fractional Camassa–Holm equation, Nonlocal elasticity, Improved Boussinesq equation, Asymptotic expansions
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0375-9601
Kayıt Numarası	787d34b0-d310-48e1-a990-348e53bdd96c
Lokasyon	Natural and Mathematical Sciences
Tarih	2015-06-05
Örnek Metin	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

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Derivation of the Camassa-Holm equations for elastic waves

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2015-06-05

Basım Yeri - Elsevier

Konu Camassa–Holm equation, Fractional Camassa–Holm equation, Nonlocal elasticity, Improved Boussinesq equation, Asymptotic expansions

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0375-9601

Kayıt Numarası 787d34b0-d310-48e1-a990-348e53bdd96c

Lokasyon Natural and Mathematical Sciences

Tarih 2015-06-05

Örnek Metin 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