English

Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals

Exactly Solvable and Integrable Systems 2022-05-19 v3 Mathematical Physics math.MP

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

Cite

@article{arxiv.2110.03317,
  title  = {Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals},
  author = {Si-Qi Liu and Zhe Wang and Youjin Zhang},
  journal= {arXiv preprint arXiv:2110.03317},
  year   = {2022}
}