English

Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method

Mathematical Physics 2022-05-04 v1 math.MP Exactly Solvable and Integrable Systems

Abstract

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary tau-function in terms of matrix resolvents. As an application, we provide a way of computing certain integrals over the unitary group.

Keywords

Cite

@article{arxiv.2112.14202,
  title  = {Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method},
  author = {Mattia Cafasso and Di Yang},
  journal= {arXiv preprint arXiv:2112.14202},
  year   = {2022}
}

Comments

15 pages

R2 v1 2026-06-24T08:33:48.560Z