@article{f929aad8260d425a9df5c39928ebbb2c,
title = "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.",
keywords = "Cnoidal waves, Finite element method, Solitary waves, Stability",
author = "Dimitrios Mitsotakis and Denys Dutykh and John Carter",
note = "Funding Information: D. Mitsotakis thanks Professor Boaz Ilan for suggestions, comments, and stimulating discussions related to dispersive waves. The authors acknowledge the invaluable help of Professor Paul Milewski for discussions related to the numerical schemes for the Euler equations and Professor Didier Clamond for discussions on pseudo-spectral methods. J. Carter was supported by the National Science Foundation under grant number DMS-1107476 . D. Mitsotakis was supported by the Marsden Fund administered by the Royal Society of New Zealand with contract number VUW1418 . Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2017",
month = apr,
day = "1",
doi = "10.1016/j.wavemoti.2016.09.008",
language = "British English",
volume = "70",
pages = "166--182",
journal = "Wave Motion",
issn = "0165-2125",
publisher = "Elsevier B.V.",
}