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

Denys Dutykh 1, 2, 3 Mark Hoefer 4 Dimitrios Mitsotakis 5
1 LAMA - Laboratoire de Mathématiques
2 INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 University of Colorado - Department of Applied Mathematics
5 Victoria University of Wellington
Abstract : 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.
Keywords : Serre equations surface tension solitary waves peakons
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Submitted on : Thursday, April 12, 2018 - 8:37:41 PM
Last modification on : Friday, November 6, 2020 - 3:26:59 AM

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CNRS | INSMI | TDS-MACS | UNIV-SAVOIE | LAMA | UGA

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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. Theoretical and Computational Fluid Dynamics, Springer Verlag, 2018, 32 (3), pp.371-397. ⟨10.1007/s00162-018-0455-3⟩. ⟨hal-01465356v2⟩

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