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Dispersionless DKP hierarchy and elliptic Lowner equation
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Dispersionless DKP hierarchy and elliptic Lowner equation
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We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and show that they are described by an elliptic version of the Lowner equation. With a particular choice of the driving function, the latter appears to be closely related to the Painleve VI equation with special choice of parameters.
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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