Symmetry analysis and new partially invariant solutions for the gas dynamics system with a special equation of state

This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the “podmodeli” (submodels) program outlined by Ovsyannikov (1994). We consider the case of a specific equation of state, prescribing pressure to be the sum of entropy and an arbitrary function of density. Such a system has a 12-dimensional symmetry Lie algebra. This work advances the study of its four-dimensional subalgebras, continuing the investigation initiated in Siraeva (2024). For a large subset of previously unconsidered, non-similar four-dimensional subalgebras from an optimal list, we compute a complete set of generating invariants. For one of the subalgebras, we construct and explicitly solve a partially symmetry-reduced system (submodel). This yields new families of explicit solutions for the original system, the trajectories of which are then analyzed. Additionally, we match each of the subalgebras considered in this paper with its isomorphism class, laying the groundwork for future study of the hierarchy of the reduced systems.