Symmetry properties of a system of Euler-type equations for magnetized plasmas

We provide all Lie point symmetries of a system of partial differential equations, of great interest to plasma physics; we deduce the corresponding invariant solutions and discuss their physical interpretation. We also consider some of its conditional and partial symmetries and obtain other interesting solutions. Finally, we point out that, although the system can be cast in divergence form and admits conserved currents, it does not admit potential symmetries