“Simple” solutions of the equations of dynamics for a polytropic gas

The notion of a “simple” solution of a system of differential equations that admit a local Lie group $G$ of transformations of the basic space is considered as an invariant $H$-solution of type $(0,0)$ with respect to the subgroup $H\subset G$. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.