Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit

TL;DR

This paper demonstrates that the dispersionless limits of Pfaff integrable hierarchies can be reformulated using elliptic functions, revealing their structure as elliptic deformations of well-known hierarchies.

Contribution

It introduces an elliptic reformulation of the dispersionless Pfaff-KP and Pfaff-Toda hierarchies, providing new insights into their structure and connections to elliptic functions.

Findings

Dispersionless Pfaff hierarchies admit elliptic function reformulation

Elliptic form acts as deformation of KP and 2D Toda hierarchies

Reveals geometric structure of integrable hierarchies

Abstract

We show that the dispersionless limits of the Pfaff-KP (also known as the DKP or Pfaff lattice) and the Pfaff-Toda hierarchies admit a reformulation through elliptic functions. In the elliptic form they look like natural elliptic deformations of the KP and 2D Toda hierarchy respectively.