Mathematical modeling and numerical analysis for the higher order Boussinesq system

Bashar Bhorbatly (1) , Ralph Lteif (2) , Samer Israwi (3) , Stéphane Gerbi (4)

1 Department of Industrial and Mechanical Engineering [Byblos]
2 CSM/SAS/LAU - Department of Computer Science and Mathematics [Lebanese American University]
3 Department of Mathematics [Beirut]
4 LAMA - Laboratoire de Mathématiques

This study deals with higher-ordered 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 $1/\sqrt{\eps}$ 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.

Mots clés: Water waves; Boussinesq system; higher-order asymptotic model; well-posedness; traveling waves; explicit solution; numerical validation; February 2; 2022. 2010 Mathematics Subject Classification. 35Q35; 35L45; 35L60; 76B45; 76B55; 35C07; 65L99 Water waves

Domaines: Equations aux dérivées partielles [math.AP]

Bashar Bhorbatly, Ralph Lteif, Samer Israwi, Stéphane Gerbi. Mathematical modeling and numerical analysis for the higher order Boussinesq system. 2021. ⟨hal-03142052v2⟩