Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations

Name: Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2015
Basım Yeri	- Estonian Academy of Sciences
Konu	nonlocal elasticity, Korteweg–de Vries equation, Benjamin–Bona–Mahony equation, Camassa–Holm equation, fractional Camassa–Holm equation
Tür	Belge
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	2-s2.0-84947804639
Kayıt Numarası	1fd9d3c8-37f8-4bc7-9cfb-b6854cfaa518
Lokasyon	Natural and Mathematical Sciences
Tarih	2015
Örnek Metin	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

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Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: The KdV, BBM and CH equations

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

Basım Tarihi 2015

Basım Yeri - Estonian Academy of Sciences

Konu nonlocal elasticity, Korteweg–de Vries equation, Benjamin–Bona–Mahony equation, Camassa–Holm equation, fractional Camassa–Holm equation

Tür Belge

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 2-s2.0-84947804639

Kayıt Numarası 1fd9d3c8-37f8-4bc7-9cfb-b6854cfaa518

Lokasyon Natural and Mathematical Sciences

Tarih 2015

Örnek Metin 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