Grassmann-valued fluid dynamics

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Abstract
Certain systems of nonlinear partial differential equations can be written in a simple form as a single Grassmann‐valued partial differential equation.Equations describing compressible fluid flow are of this type. A method for finding soft solutions of the Grassmann‐valued partial differential equation arising in this context is presented. The method is a generalization of the Lagrangian‐coordinates approach to the case of Grassmann variables. Generally, solutions obtained by this method have the form of infinite series, whose expansion yields new relations among the unknown variables. In some simple cases, the series can be summed. The equivalence of the Grassmann solutions to the usual solutions is shown for these cases.