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 -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.
Keywords
Cite
@article{arxiv.2407.12424,
title = {Multicomponent DKP hierarchy and its dispersionless limit},
author = {A. Savchenko and A. Zabrodin},
journal= {arXiv preprint arXiv:2407.12424},
year = {2024}
}
Comments
22 pages, no figures