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 allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals. 
A. M. Grundland, A. J. Hariton