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

作　　者：Gayaz Khakimzyanov Denys Dutykh Zinaida Fedotova Dimitrios Mitsotakis 

机构地区：[1]Institute of Computational Technologies,Siberian Branch of the Russian Academy of Sciences,Novosibirsk 630090,Russia [2]LAMA,UMR 5127 CNRS,UniversitéSavoie Mont Blanc,Campus Scientifique,73376 Le Bourget-du-Lac Cedex,France [3]Victoria University of Wellington,School of Mathematics,Statistics and Operations Research,PO Box 600,Wellington 6140,New Zealand

出　　处：《Communications in Computational Physics》2018年第1期1-29,共29页计算物理通讯（英文）

基　　金：This research was supported by RSCF project No 14-17-00219.D.Mitsotakis was supported by the Marsden Fund administered by the Royal Society of New Zealand.

摘　　要：In this paperwe reviewthe 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.

关 键 词：Long wave approximation nonlinear dispersive waves shallow water equations solitary waves 

分 类 号：O17[理学—数学]