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.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 9 Nov 2017|
- dispersionlesss DKP hierarchy
- Egorov type metric
- elliptic Löwner equation
- GibbonsTsarev equation
- multi-variable reduction