Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit

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.

13 pages, no figures, written for proceedings of the 4th Workshop on combinatorics of moduli spaces, cluster algebras, and topological recursion (Moscow, May 2014); minor changes

References in corpus (3)

• Theta vocabulary I
• N-soliton solutions to the DKP equation and Weyl group actions
• Dispersionless DKP hierarchy and elliptic Lowner equation

Cited by in corpus (4)

• Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains
• Multi-variable reductions of the dispersionless DKP hierarchy
• Loewner equations and reductions of dispersionless hierarchies
• Dispersionless Pfaff-Toda hierarchy and elliptic Löwner equation