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Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space

Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space

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.

Author Details

Gayaz Khakimzyanov Email

Denys Dutykh Email

Zinaida Fedotova Email

Dimitrios Mitsotakis Email

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