Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit

We show that the dispersionless limits of the Pfaff–KP {(}also known as the $D$KP or Pfaff lattice{)} and the Pfaff–Toda hierarchies admit a reformulation in terms of elliptic functions. In the elliptic form, they look like natural elliptic deformations of the respective dispersionless KP and two-dimensional Toda hierarchies.