# Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space

## TL;DR

This paper reviews the development of dispersive shallow water wave models, focusing on classical and improved Boussinesq and Serre-Green-Naghdi equations, and proposes a unified modeling framework on a flat space.

## Contribution

It introduces a unified framework for dispersive wave models, consolidating various well-known equations, and sets the stage for future numerical discretization on adaptive grids.

## Key findings

- Comprehensive review of dispersive wave models
- Proposal of a unified modeling framework
- Foundation for numerical methods on adaptive grids

## Abstract

In this paper, we review the history and current state-of-the-art in the 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.