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Volume 23, Issue 1
Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space

Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova & Dimitrios Mitsotakis

DOI: 10.4208/cicp.OA-2016-0179a

Commun. Comput. Phys., 23 (2018), pp. 1-29.

Published online: 2018-01

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  • 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.

  • Keywords

Long wave approximation, nonlinear dispersive waves, shallow water equations, solitary waves.

  • AMS Subject Headings

76B15, 76B25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-23-1, author = {Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova and Dimitrios Mitsotakis}, title = {Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0179a}, url = {http://global-sci.org/intro/article_detail/cicp/10519.html} }
TY - JOUR T1 - Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space AU - Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova & Dimitrios Mitsotakis JO - Communications in Computational Physics VL - 1 SP - 1 EP - 29 PY - 2018 DA - 2018/01 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0179a UR - https://global-sci.org/intro/article_detail/cicp/10519.html KW - Long wave approximation, nonlinear dispersive waves, shallow water equations, solitary waves. AB -

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.

Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova and Dimitrios Mitsotakis. (2018). Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space. Communications in Computational Physics. 23 (1). 1-29. doi:10.4208/cicp.OA-2016-0179a
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