Multicomponent DKP hierarchy and its dispersionless limit

Abstract

Using the free fermions technique and bosonization rules, we introduce the multicomponent DKP hierarchy as a generating bilinear integral equation for the tau-function. A number of bilinear equations of the Hirota–Miwa type are obtained as its corollaries. We also consider the dispersionless version of the hierarchy as a set of nonlinear differential equations for the dispersionless limit of logarithm of the tau-function (the F-function). We show that there is an elliptic curve built in the structure of the hierarchy, with the elliptic modulus being a dynamical variable. This curve can be uniformized by elliptic functions, and in the elliptic parametrization many dispersionless equations of the Hirota–Miwa type become equivalent to a single equation having a nice form.