Structure and evolution of the 1D and 2D solitons on shallow fluid with varying relief of bottom

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 wave-length 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.