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arXiv · 2510.04151

Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold

Haonan Qu·Qiulan Zhao
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Abstract

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.

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Haonan Qu, Qiulan Zhao. 2025-10-05. Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold. https://arxiv.org/abs/2510.04151

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