Dispersionless DKP hierarchy and elliptic Lowner equation

Abstract

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.

arXiv comment15 pages

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Cited by in corpus (5)

• Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit
• Multi-variable reductions of the dispersionless DKP hierarchy
• Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation
• Loewner equations and reductions of dispersionless hierarchies
• Dispersionless Pfaff-Toda hierarchy and elliptic Löwner equation