Multi-variable reductions of the dispersionless DKP hierarchy

V. Akhmedova, T. Takebe, A. Zabrodin

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2 Citations (Scopus)

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.

Original languageEnglish
Article number485204
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number48
DOIs
Publication statusPublished - 9 Nov 2017
Externally publishedYes

Keywords

  • dispersionlesss DKP hierarchy
  • Egorov type metric
  • elliptic Löwner equation
  • GibbonsTsarev equation
  • multi-variable reduction

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