Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911192310611968 |
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| author | Qu, Haonan Zhao, Qiulan |
| author_facet | Qu, Haonan Zhao, Qiulan |
| contents | We study the local bihamiltonian structures of the asymmetric rational reductions of the 2D-Toda hierarchy (RR2T) of types $(2,1)$ and $(1,2)$ at the full-dispersive level, and construct a three-dimensional generalized Frobenius manifold with non-flat unity associated with the $(2,1)$-type. Furthermore, we explicitly relate the $(2,1)$-type RR2T to the bi-graded Toda and constrained KP hierarchies via linear reciprocal and Miura-type transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold Qu, Haonan Zhao, Qiulan Exactly Solvable and Integrable Systems Mathematical Physics Differential Geometry We study the local bihamiltonian structures of the asymmetric rational reductions of the 2D-Toda hierarchy (RR2T) of types $(2,1)$ and $(1,2)$ at the full-dispersive level, and construct a three-dimensional generalized Frobenius manifold with non-flat unity associated with the $(2,1)$-type. Furthermore, we explicitly relate the $(2,1)$-type RR2T to the bi-graded Toda and constrained KP hierarchies via linear reciprocal and Miura-type transformations. |
| title | Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2510.04151 |