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 ...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.展开更多
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.
文摘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.
