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Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit

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arxiv 1412.8435 v2 pith:4C2T4QXY submitted 2014-12-29 math-ph math.MPnlin.SI

V.Akhmedova , A.Zabrodin This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords elliptichierarchiespfaffadmitdeformationsdispersiondispersionlessform
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dispersionless modified DKP hierarchy as the Yang-Baxter equation

    nlin.SI 2026-07 accept novelty 8.0 of 10

    Dispersionless modified DKP hierarchy is equivalent to the Yang-Baxter equation for Baxter's elliptic R-matrix of Boltzmann weights for the 8-vertex model.

  2. Integrable hierarchies with zero dispersion and elliptic curves

    nlin.SI 2026-05 unverdicted novelty 6.0 of 10

    Dispersionless limits of KP, Toda, and Pfaff-type hierarchies possess a dynamical algebraic curve (genus 0 or 1) that can be uniformized by rational, trigonometric, or elliptic functions.

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