| Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 593 - 615 | |
| DOI | https://doi.org/10.1051/m2an/2022015 | |
| Published online | 03 March 2022 | |
Mathematical modeling and numerical analysis for the higher order Boussinesq system
1
Lebanese American University (LAU), Graduate Studies and Research (GSR), School of Arts and Sciences, Computer Science and Mathematics Department, Beirut, Lebanon
2
Lebanese University, Laboratory of Mathematics-EDST, Department of Mathematics, Faculty of Sciences 1, Beirut, Lebanon
3
Laboratoire de Mathématiques UMR 5127 CNRS & Université de Savoie Mont Blanc, Campus scientifique, 73376 Le Bourget du Lac Cedex, France
* Corresponding author: ralph.lteif@lau.edu.lb
Received:
29
January
2021
Accepted:
31
January
2022
This study deals with higher-order asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and uniqueness of solution on a relevant time scale of order 1/√ε and showing that the solution’s behavior is close to the solution of the water waves equations with a better precision corresponding to initial data, the asymptotic model is well-posed in the sense of Hadamard. Then we compared several water waves solitary solutions with respect to the numerical solution of our model. At last, we solve explicitly this model and validate the results numerically.
Mathematics Subject Classification: 35Q35 / 35L45 / 35L60 / 76B45 / 76B55 / 35C07 / 65L99
Key words: Water waves / Boussinesq system / higher-order asymptotic model / well-posedness / traveling waves / explicit solution / numerical validation
© The authors. Published by EDP Sciences, SMAI 2022
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