The method has been developed for separation of the total hydrodynamic field into components: stationary one and those moving in opposite directions. Thus the set of equations breaks into three nonlinear equations for interacting components. New equations describing slightly linear interaction have been derived for the general form of the refined equation of state. The calculated nonlinear evolution of directed components shows that a directed wave in liquid keeps its direction even at high amplitudes of initial distortions. Solution of the problem is also interesting in view of a wide variety of problems with similar dispersion relation. The integral dispersion operator, whose form is determined by medium inhomogeneity, arises also in the theory of waveguide propagation of electromagnetic waves. The directed and stationary waves change the background temperature (and density), as well as the main refractive index and thus create moving or stationary areas of induced refraction and scattering of optical waves.