On one manner of constructing exact solutions of quasi-hydrodynamic system

A new approach to constructing exact solutions of the Cauchy problem for the quasi-hydrodynamic system is proposed. Substitutions are selected that satisfy the three derived conditions. Examples of using the proposed approach are given. Particular attention is paid to solutions of the quasi-hydrodynamic system that do not satisfy either the Navier-Stokes or Euler equations. For the first time, such a solution to the Cauchy problem with variable pressure is constructed.