Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2017-06
Publication Place
-
American Institute of Mathematical Sciences
Subject
Camassa-Holm equation, Improved Boussinesq equation, Nonlocal wave equation, Rigorous justification
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1553-5231
Record ID
ca226806-1d57-42b9-b3ab-a514b2cd11ef
Library Location
Natural and Mathematical Sciences
Date
2017-06
Sample Text
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
