On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations

Name: On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2017-06
Basım Yeri	- American Institute of Mathematical Sciences
Konu	Camassa-Holm equation, Improved Boussinesq equation, Nonlocal wave equation, Rigorous justification
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1553-5231
Kayıt Numarası	ca226806-1d57-42b9-b3ab-a514b2cd11ef
Lokasyon	Natural and Mathematical Sciences
Tarih	2017-06
Örnek Metin	We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and dispersion. Our results demonstrate that, in the present regime, any solution of the improved Boussinesq equation is split into two waves propagating in opposite directions independently, each of which is governed by the Camassa-Holm equation. We observe that the approximation error for the decoupled problem considered in the present study is greater than the approximation error for the unidirectional problem characterized by a single Camassa-Holm equation. We also consider lower order approximations and we state similar error estimates for both the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.
DOI	10.3934/dcds.2017133
Cilt	37

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On the decoupling of the improved Boussinesq equation into two uncoupled Camassa-Holm equations

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

Basım Tarihi 2017-06

Basım Yeri - American Institute of Mathematical Sciences

Konu Camassa-Holm equation, Improved Boussinesq equation, Nonlocal wave equation, Rigorous justification

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1553-5231

Kayıt Numarası ca226806-1d57-42b9-b3ab-a514b2cd11ef

Lokasyon Natural and Mathematical Sciences

Tarih 2017-06

Örnek Metin We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and dispersion. Our results demonstrate that, in the present regime, any solution of the improved Boussinesq equation is split into two waves propagating in opposite directions independently, each of which is governed by the Camassa-Holm equation. We observe that the approximation error for the decoupled problem considered in the present study is greater than the approximation error for the unidirectional problem characterized by a single Camassa-Holm equation. We also consider lower order approximations and we state similar error estimates for both the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.

DOI 10.3934/dcds.2017133

Cilt 37