PHASE AND AMPLITUDE CHARACTERISTICS OF HIGHER-ACCURACY NONLINEAR DISPERSIVE MODELS.

Properties of dispersion relations for two new fully nonlinear weakly dispersive shallow water models are studied. For these models, it is possible to use certain parameters to obtain the fourth, sixth, or eighth order of accuracy of phase velocity approximation of the three-dimensional potential flow model. For the hierarchy of shallow water models, with the assumption of slight changes in the bottom shape, formulas are obtained that establish a relationship between the variation rate of the wave amplitude and that of the fluid layer thickness; also, the dependences of the amplitude and length of an incoming wave on the water region depth are derived. It is shown that the new model of the fourth-order long-wave approximation with the eighth order of accuracy of the dispersion relation provides the best approximation of considered characteristics in the case of bottoms of both horizontal and variable shape. [ABSTRACT FROM AUTHOR]