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<p>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 <i>F</i>-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.</p>

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Multicomponent DKP hierarchy and its dispersionless limit

  • 期刊论文

  • 发表日期：

    2025年2月27日

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  • A. Savchenko,
  • A. Zabrodin

摘要

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.