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

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.

33 pages, 1 figure, 79 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (1)

• Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry

Cited by in corpus (5)

• Dispersive shock waves theory for non-integrable equations
• Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry
• Peregrine's system revisited
• Conservative invariant finite-difference schemes for the modified shallow water equations in Lagrangian coordinates
• Group classification of the two-dimensional Green-Naghdi equations with a time dependent bottom topography