Multi-variable reductions of the dispersionless DKP hierarchy

Abstract

We consider multi-variable reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. The reduction is given by a system of elliptic Löwner equations supplemented by a system of partial differential equations of hydrodynamic type. The compatibility conditions for the elliptic Löwner equations are derived. They are elliptic analogues of the Gibbons-Tsarev equations. We prove solvability of the hydrodynamic type system by means of the generalized hodograph method. The associated diagonal metric is proved to be of the Egorov type.

24 pages, no figures

References in corpus (6)

• Theta vocabulary I
• N-soliton solutions to the DKP equation and Weyl group actions
• Löwner equations and dispersionless hierarchies
• Dispersionless DKP hierarchy and elliptic Lowner equation
• Systems of Gibbons-Tsarev type and integrable 3-dimensional models
• Integrable pseudopotentials related to elliptic curves