Reductions of the dispersionless DKP hierarchy

We describe reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. Multi-variable reduction is given by a system of elliptic Löwner equations supplemented by a system of partial differential equations of hydrodynamic type. The compatibility conditions for the elliptic Löwner equations are elliptic analogues of the Gibbons–Tsarev equations.