Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908859258372096 |
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| author | Feng, Zongyao Geng, Lumin Wu, Chao-Zhong |
| author_facet | Feng, Zongyao Geng, Lumin Wu, Chao-Zhong |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_01354 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy Feng, Zongyao Geng, Lumin Wu, Chao-Zhong Exactly Solvable and Integrable Systems 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. |
| title | Additional symmetries of the KP-mKP hierarchy and Virasoro constraints to the Burgers-KdV hierarchy |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.01354 |