On the nonlinear dynamics of the traveling-wave solutions of the Serre system
Résumé
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge-Kutta methods in time. Other forms of solutions such as cnoidal waves and dispersive shock waves are also considered. The differences between solutions of the Serre equations and the Euler equations are also studied.
Domaines
Mécanique des fluides [physics.class-ph] Mécanique des fluides [physics.class-ph] Milieux et Changements globaux Systèmes Solubles et Intégrables [nlin.SI] Formation de Structures et Solitons [nlin.PS] Hydrologie Dynamique des Fluides [physics.flu-dyn] Physique Atmosphérique et Océanique [physics.ao-ph] Analyse numérique [math.NA] Equations aux dérivées partielles [math.AP] Physique Numérique [physics.comp-ph] Océan, Atmosphère Géophysique [physics.geo-ph] Géophysique [physics.geo-ph]| Origine | Fichiers produits par l'(les) auteur(s) |
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