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arXiv · 2306.09115

The constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type

Ang Fu·Di Yang·Dafeng Zuo
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Abstract

In this paper, we extend the matrix-resolvent method to the study of the Dubrovin--Zhang type tau-functions for the constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type. We show that the Dubrovin--Zhang type tau-function of an arbitrary solution to the bigraded Toda hierarchy of $(M,1)$-type is a Dubrovin--Zhang type tau-function for the constrained KP hierarchy, which generalizes the result in [10, 35] for the Toda lattice hierarchy and the NLS hierarchy corresponding to the $M=1$ case.

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Ang Fu, Di Yang, Dafeng Zuo. 2023-06-15. The constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type. https://arxiv.org/abs/2306.09115

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