The nonlinear equations of hydrodynamic type featuring effects of nonlinear self-action and interactions of nonlinear acoustic hydrodynamic-type fields are considered. These equations, complemented by the continuity equation, describe the evolution of a passive and active tracer in moving continuous media. It is shown that the solutions of the mentioned nonlinear equations with arbitrary initial conditions are reduced to the solutions of a system of linear diffusion equations. It allows to investigate in detail the dynamic and statistical characteristics of nonlinear interaction of acoustic waves in a model polytropic gas, and also to analyze behavior of density fields and effects of diffusion and transport of particles in nonlinear fields of hydrodynamic type. ©2000 American Institute of Physics.