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

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.
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https://hal.archives-ouvertes.fr/hal-01465356
Contributor : Denys Dutykh <>
Submitted on : Thursday, April 12, 2018 - 8:37:41 PM
Last modification on : Tuesday, December 17, 2019 - 10:04:18 AM

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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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