Solitons on a shallow fluid of variable depth

Abstract

The results of numerical study of evolution of the solitons of gravity and gravity-capillary waves on the surface of a shallow uid, when the characteristic wavelength is essentially greater than the depth, λ ≫ H, are presented for the cases when dispersive parameter is a function of time, and the spatial coordinates β = β (t; x; y). This corresponds to the problems when the relief of the bottom is changed in time and space. We use both the one-dimensional approach (the equations of the KdV-class) and also two-dimensional description (the equations of the KP-class), in case of need.