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.
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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}
}
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15 pages