Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations |
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Authors: | Denys Dutykh Mark Hoefer Dimitrios Mitsotakis |
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Institution: | 1.LAMA, UMR 5127 CNRS,Université Savoie Mont Blanc,Le Bourget-du-Lac Cedex,France;2.Department of Applied Mathematics,University of Colorado,Boulder,USA;3.School of Mathematics and Statistics,Victoria University of Wellington,Wellington,New Zealand |
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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 traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge–Kutta method of order 4. |
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