Dynamics of Interaction of Two Soliton Clouds

On the basis of relationship between the kinetic equation for two soliton clouds in the theory of the Korteweg-de Vries equation and equations of the Chaplygin gas dynamics it is shown that the existence of waves propagating without a change in their form is a fundamental property of the nonlinear dynamics of soliton gases. The solutions of several typical problems in the soliton gas dynamics are considered and characteristic features of such dynamics, which make it possible to estimate the effects of interaction of soliton gases, are indicated.