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

Gayaz Khakimzyanov ,  Denys Dutykh ,  Zinaida Fedotova and Dimitrios Mitsotakis


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

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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.

  • History

Published online: 2018-01

  • AMS Subject Headings

76B15, 76B25

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