Erbay, Hüsnü A. and Erbay, Saadet and Erkip, Albert (2017) On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations. Discrete and Continuous Dynamical Systems, 37 (6). pp. 31113122. ISSN 10780947 (Print) 15535231 (Online)
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Official URL: http://dx.doi.org/10.3934/dcds.2017133
Abstract
We rigorously establish that, in the longwave regime characterized by the assumptions of long wavelength and small amplitude, bidirecdional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled CamassaHolm 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 CamassaHolm 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 CamassaHolm equation. We also consider lower order approximations and we state similar error estimates for both the BenjaminBonaMahony approximation and the Kortewegde Vries approximation.
Item Type:  Article 

Uncontrolled Keywords:  CamassaHolm equation, improved Boussinesq equation, nonlocal wave equation, rigorous justification 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Albert Erkip 
Date Deposited:  15 Mar 2017 15:51 
Last Modified:  15 May 2017 11:43 
URI:  https://research.sabanciuniv.edu/id/eprint/31092 
Available Versions of this Item

On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations. (deposited 30 Jan 2017 16:00)
 On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations. (deposited 15 Mar 2017 15:51) [Currently Displayed]