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

Author:

Ang Fu, Di Yang, Dafeng Zuo

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

date:

2023-06-14 16:00:00

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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