Derivation of generalized Camassa-Holm equations from Boussinesq-type equations

Name: Derivation of generalized Camassa-Holm equations from Boussinesq-type equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Derivation of generalized Camassa-Holm equations from Boussinesq-type equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2016
Basım Yeri	- Informa Group
Konu	Generalized Camassa-Holm equation, Modified Camassa-Holm equation, Fractional Camassa-Holmequation, Improved Boussinesq equation, Asymptotic expansions
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1776-0852
Kayıt Numarası	3e1c4ab9-94df-47e7-b732-f4c8500db360
Lokasyon	Natural and Mathematical Sciences
Tarih	2016
Örnek Metin	In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive effects and strictly following the arguments in the asymptotic derivation of the classical CH equation. The resulting equations generalize the CH equation in two different ways. The first generalization replaces the quadratic nonlinearity of the CH equation with a general power-type nonlinearity while the second one replaces the dispersive terms of the CH equation with fractional-type dispersive terms. In the absence of both higher-order nonlinearities and fractional-type dispersive effects, the generalized equations derived reduce to the classical CH equation that describes unidirectional propagation of shallow water waves. The generalized equations obtained are compared to similar equations available in the literature, and this leads to the observation that the present equations have not appeared in the literature.
DOI	10.1080/14029251.2016.1199493
Cilt	23

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Derivation of generalized Camassa-Holm equations from Boussinesq-type equations

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

Basım Tarihi 2016

Basım Yeri - Informa Group

Konu Generalized Camassa-Holm equation, Modified Camassa-Holm equation, Fractional Camassa-Holmequation, Improved Boussinesq equation, Asymptotic expansions

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1776-0852

Kayıt Numarası 3e1c4ab9-94df-47e7-b732-f4c8500db360

Lokasyon Natural and Mathematical Sciences

Tarih 2016

Örnek Metin In this paper we derive generalized forms of the Camassa-Holm (CH) equation from a Boussinesq-type equation using a two-parameter asymptotic expansion based on two small parameters characterizing nonlinear and dispersive effects and strictly following the arguments in the asymptotic derivation of the classical CH equation. The resulting equations generalize the CH equation in two different ways. The first generalization replaces the quadratic nonlinearity of the CH equation with a general power-type nonlinearity while the second one replaces the dispersive terms of the CH equation with fractional-type dispersive terms. In the absence of both higher-order nonlinearities and fractional-type dispersive effects, the generalized equations derived reduce to the classical CH equation that describes unidirectional propagation of shallow water waves. The generalized equations obtained are compared to similar equations available in the literature, and this leads to the observation that the present equations have not appeared in the literature.

DOI 10.1080/14029251.2016.1199493

Cilt 23