Matrix resolvent and the discrete KdV hierarchy
Mathematical Physics
2020-07-15 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice hierarchy. Explicit formulae for generating series of logarithmic derivatives of the tau-functions are then obtained, and applications to enumeration of ribbon graphs with even valencies and to the special cubic Hodge integrals are considered.
Cite
@article{arxiv.1903.11578,
title = {Matrix resolvent and the discrete KdV hierarchy},
author = {Boris Dubrovin and Di Yang},
journal= {arXiv preprint arXiv:1903.11578},
year = {2020}
}
Comments
It was added a remark after Theorem 1; added Appendix A; added references; two statements moved to Introduction; corrected typos. 26 pages