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arXiv · 2603.01354

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

Zongyao Feng·Lumin Geng·Chao-Zhong Wu
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Abstract

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.

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Zongyao Feng, Lumin Geng, Chao-Zhong Wu. 2026-03-02. Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy. https://arxiv.org/abs/2603.01354

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