On some classes of solutions of aerohydromechanic equations

The article gives a review of the method of constructing parametric solutions of polynomial form for systems of partial differential equations and its application to some aerohydromechanic equations. For example the parametric solutions are constructed and their classification is carried out for the system of equations, describing the plane flows of the ideal gas with the constant entropy. Particularly, the solutions of “simple wave” type are demonstrated. Also the solutions of transonic equations, describing flows of gas with local supersonic zones in Laval nozzles are obtained.