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In this paper, a supersymmetric extension of the polytropic gas dynamicsequations is constructed through the use of a superspace involving twoindependent fermionic variables and two bosonic superfields. A superalgebra ofsymmetries of the proposed extended model is determined and a systematicclassification of the one-dimensional subalgebras of this superalgebra isperformed. Through the use of the symmetry reduction method, a number ofinvariant solutions of the supersymmetric polytropic gas dynamics equations arefound. Several types of solutions are obtained, including algebraic-typesolutions and propagation waves (simple and double waves). Many of the obtainedsolutions involve arbitrary functions of one or two bosonic or fermionicvariables. In the case where the arbitrary functions involve only theindependent fermionic variables, the solutions are expressed in terms of Taylorexpansions.

Supersymmetric formulation of polytropic gas dynamics and its invariant solutions