Dispersionless DKP hierarchy and the elliptic Löwner equation

Abstract

We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and show that they are described by an elliptic version of the Löwner equation. With a particular choice of the driving function, the latter appears to be closely related to the Painlevé VI equation with a special choice of parameters.