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

In this paper, a supersymmetric extension of a system of hydrodynamic-type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allows us to construct several classes of invariant solutions, including traveling waves, centered waves, and solutions involving monomials, exponentials, and radicals