The compression of gas followed by expansion

We consider the system of gas dynamics equations with the state equation of the monatomic gas. The system admits a group of transformations with a 14-dimensional Lie algebra. A projective operator is specific to this algebra. We consider the invariant submodel on two-dimensional subalgebra containing the projective operator. For the vorticity-free motions, the submodel is reduced to an overdetermined system of three equations. A particular solution is found for it, physical interpretation is given, and trajectories of gas particles are depicted. The solution gives the gas compression followed by expansion.