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<p>A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional symmetries. Moreover, the additional symmetries are represented as certain linear actions on the tau functions of the hierarchy, with the help of the Adler-Shiota-van Moerbeke formula. As an application, we reprove the Virasoro constraints to the tau functions of the Burgers-KdV hierarchy, and such results are generalized to its higher order extensions regarded as reductions of the KP-mKP hierarchy.</p>

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Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • Zongyao Feng,
  • Lumin Geng,
  • Chao-Zhong Wu

摘要

A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional symmetries. Moreover, the additional symmetries are represented as certain linear actions on the tau functions of the hierarchy, with the help of the Adler-Shiota-van Moerbeke formula. As an application, we reprove the Virasoro constraints to the tau functions of the Burgers-KdV hierarchy, and such results are generalized to its higher order extensions regarded as reductions of the KP-mKP hierarchy.