On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations
Erbay, Hüsnü A. and Erbay, Saadet and Erkip, Albert (2017) On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations. (Accepted/In Press) AbstractWe 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. Available Versions of this Item On the decoupling of the improved boussinesq equation into two uncoupled CamassaHolm equations. (deposited 30 Jan 2017 16:00) [Currently Displayed]
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