TY - JOUR T1 - Dispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat Space 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.