Invariant solutions of the special model of fluids with internal inertia

This paper is devoted to the detailed study one of the models, obtained in [Hematulin A, Meleshko SV, Gavrilyuk SG. Group classification of one-dimensional equations of fluids with internal inertia. Math Meth Appl Sci 2007;30:2101-20] by group analysis. The main feature of this model is that the equations describing the motion of fluids with the potential function W=-αρ-3ρ˙2+βρ3 admit projective transformations. Optimal systems of subalgebras are constructed. Representations of all invariant solutions are obtained.