Year: 2018
Author: Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova, Dimitrios Mitsotakis
Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 1–29
Abstract
In this paper we review the history and current state-of-the-art in modelling of long nonlinear dispersive waves. For the sake of conciseness of this review we omit the unidirectional models and focus especially on some classical and improved BOUSSINESQ-type and SERRE–GREEN–NAGHDI equations. Finally, we propose also a unified modelling framework which incorporates several well-known and some less known dispersive wave models. The present manuscript is the first part of a series of two papers. The second part will be devoted to the numerical discretization of a practically important model on moving adaptive grids.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0179a
Communications in Computational Physics, Vol. 23 (2018), Iss. 1 : pp. 1–29
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Long wave approximation nonlinear dispersive waves shallow water equations solitary waves.
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