نویسنده
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
تاریخ انتشار
2017-06
محل انتشار
-
American Institute of Mathematical Sciences
موضوع
Camassa-Holm equation, Improved Boussinesq equation, Nonlocal wave equation, Rigorous justification
نوع
دوره ای
زبان
انگلیسی
دیجیتال
بله
نسخه خطی
خیر
کتابخانه
دانشگاه اوزیغین
شناسه دارایی کتابخانه
1553-5231
شماره ثبت
ca226806-1d57-42b9-b3ab-a514b2cd11ef
محل کتابخانه
Natural and Mathematical Sciences
تاریخ
2017-06
متن نمونه
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
