Solitons on shallow fluid with variable depth

Abstract

The results of numerical study of evolution of the solitons of gravity and gravity-capillary waves on surface of shallow fluid when the characteristic wavelength is essentially greater then depth, are presented for the cases when dispersive parameter is a function of time and spatial coordinates, . This corresponds to the problems when the relief of bottom is changed in time and space. We use both one-dimensional approach (the equations of the KdV-class) and also two-dimensional description (the equations of the KP-class) where it is necessary.