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In this paper, a supersymmetric extension of a system of hydrodynamic typeequations involving Riemann invariants is formulated in terms of a superspaceand superfield formalism. The symmetry properties of both the classical andsupersymmetric versions of this hydrodynamical model are analyzed through theuse of group-theoretical methods applied to partial differential equationsinvolving both bosonic and fermionic variables. More specifically, we computethe Lie superalgebras of both models and perform classifications of theirrespective subalgebras. A systematic use of the subalgebra structures allow usto construct several classes of invariant solutions, including travellingwaves, centered waves and solutions involving monomials, exponentials andradicals.

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions