Аннотация:Exact solutions and integrals of two-fluid hydrodynamic equations for a low-energy plasma motion are obtained and characteristic features of propagation for modes of a stationary form are demonstrated. The dynamics of the considered medium is described by quasi-linear evolution equations of hydrodynamic type, invariant with respect to the Galilean transformation group. Dispersion effects are associated with the presence of electrodynamic interactions in the medium. The obtained exact solutions and integrals make it possible to analyze the dynamics of subsonic and supersonic solitons and solutions such as plasma ball with a negative charge concentrated in the center. The possibility of realization of stationary plasma solutions by self-consistent electrostatic field in the own pressure is also considered in detail. An important aspect of the work is the demonstration of similar solutions in modern experimental physics.