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Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit
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Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit
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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.
Forward citations
Cited by 2 Pith papers
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Dispersionless modified DKP hierarchy as the Yang-Baxter equation
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.
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Integrable hierarchies with zero dispersion and elliptic curves
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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