Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

Denys Dutykh (1) , Mark Hoefer (2) , Dimitrios Mitsotakis (3)

1 LAMA - Laboratoire de Mathématiques
2 University of Colorado - Department of Applied Mathematics
3 Victoria University of Wellington

Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked travelling wave solutions are presented in the case of critical surface tension. The numerical experiments were performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order four.

Mots clés: Serre equations; solitary waves; surface tension; peakons

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]; Analyse numérique [math.NA]; Formation de Structures et Solitons [nlin.PS]; Systèmes Solubles et Intégrables [nlin.SI]; Physique Classique [physics.class-ph]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Dynamique des Fluides [physics.flu-dyn]

Denys Dutykh, Mark Hoefer, Dimitrios Mitsotakis. Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations. 2017. ⟨hal-01465356v1⟩