On the multi-symplectic structure of the Serre-Green-Naghdi equations

Marx Chhay (1) , Denys Dutykh (2) , Didier Clamond (3)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 LAMA - Laboratoire de Mathématiques
3 LJAD - Laboratoire Jean Alexandre Dieudonné

In this short note, we present a multi-symplectic structure of the Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in shallow water. This multi-symplectic structure allow the use of efficient finite difference or pseudo-spectral numerical schemes preserving exactly the multi-symplectic form at the discrete level.

Mots clés: Green-Naghdi model; Serre equations; fully nonlinear long waves; multi-symplectic structure

Domaines: Mécanique des fluides [physics.class-ph]; Systèmes Solubles et Intégrables [nlin.SI]; Dynamique des Fluides [physics.flu-dyn]; Physique mathématique [math-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Equations aux dérivées partielles [math.AP]

Marx Chhay, Denys Dutykh, Didier Clamond. On the multi-symplectic structure of the Serre-Green-Naghdi equations. 2015. ⟨hal-01221356v1⟩