This article is cited in 1 paper

Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals

Si-Qi  Liu, Zhe Wang, Youjin Zhang

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China

Abstract: We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the intermediate long wave hierarchy, and the remaining flows coincide with a certain limit of the flows of the fractional Volterra hierarchy which controls the special cubic Hodge integrals.

Keywords: integrable hierarchy, limit fractional Volterra hierarchy, intermediate long wave hierarchy.

MSC: 53D45, 37K10, 37K25

Received: October 28, 2021; in final form May 15, 2022; Published online May 18, 2022

Language: English

DOI: 10.3842/SIGMA.2022.037

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ArXiv: 2110.03317