On the nonlinear dynamics of the traveling-wave solutions of the Serre system

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00984035
Contributeur : Denys Dutykh <>
Soumis le : lundi 26 septembre 2016 - 19:58:22
Dernière modification le : jeudi 29 septembre 2016 - 01:17:49

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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Pas de modification 4.0 International License

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  • HAL Id : hal-00984035, version 4
  • ARXIV : 1404.6725

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Dimitrios Mitsotakis, Denys Dutykh, John D. Carter. On the nonlinear dynamics of the traveling-wave solutions of the Serre system. 28 pages, 20 figures, 3 tables, 33 references. Other author's papers can be downloaded at http://.. 2016. <hal-00984035v4>

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