A hydrodynamic nonlinear model of bubble liquid

Nonlinear equations of one-velocity bubble hydrodynamics are obtained within the framework of a general hydrodynamic description of condensed systems. The equations are valid for an arbitrary density of bubbles and do not contain description of movement of an isolated bubble, as is customary in traditional approaches. Small harmonic oscillations of the bubble medium are investigated. Existence of two longitudinal waves is shown, and the character of their dispersion and attenuation is investigated. The approach proposed is basically new, and the equations of motion differ fundamentally from the equations obtained by the method of averaging. The spectrum of one of the waves in a particular case coincides with the wave spectrum of the known theories which hold true for systems with small density of bubbles.