Multicomponent DKP hierarchy and its dispersionless limit

A. Savchenko; A. Zabrodin

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arXiv · 2407.12424

Multicomponent DKP hierarchy and its dispersionless limit

A. Savchenko·A. Zabrodin

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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.

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A. Savchenko, A. Zabrodin. 2024-07-17. Multicomponent DKP hierarchy and its dispersionless limit. https://arxiv.org/abs/2407.12424

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