Arkhipov D.G., Khabakhpashev G.A.
A new equation for the description of the transformation of two-dimensional pycnocline perturbations over fixed rigid bottom in the «solid lid» approximation is obtained. It is assumed that wave lengths are relatively large, their amplitudes are small but finite, and the bottom may be weakly sloping. The deduced equations may be applied for the simulation of the interactions between the disturbances propagating simultaneously in the opposite directions. The problem of the head-on collision of two solitary waves is solved analytically. Solutions of several characteristic problems are found numerically, and the effect of the bottom topography on the evolution of disturbances is shown.