English

Multi-variable reductions of the dispersionless DKP hierarchy

Mathematical Physics 2017-11-22 v1 math.MP Exactly Solvable and Integrable Systems

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 L\"owner equations supplemented by a system of partial differential equations of hydrodynamic type. The compatibility conditions for the elliptic L\"owner 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.

Keywords

Cite

@article{arxiv.1707.01528,
  title  = {Multi-variable reductions of the dispersionless DKP hierarchy},
  author = {V. Akhmedova and T. Takebe and A. Zabrodin},
  journal= {arXiv preprint arXiv:1707.01528},
  year   = {2017}
}

Comments

24 pages, no figures

R2 v1 2026-06-22T20:38:59.878Z