Invariant submodel of rank 1 and two families of exact solutions of gas dynamics equations with an equation of state of the special form

Abstract In this article, the gas dynamics equations with an equation of state special form are considered.The is pressure which equal to sum two functions, one being a function density, and other entropy. The system invariant under action 12-parameter transformations group. For three-dimensional subalgebra 3.32 12-dimensional Lie algebra invariants calculated, submodel rank 1 constructed, families exact solutions obtained. obtained specify motion particles in space linear velocity field inhomogeneous deformation. first family has moments time collapse. second moment collapse on plane. simplest case solutions, surface consisting particle trajectories constructed.