Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method
arXiv:2112.14202 · doi:10.1088/1751-8121/ac5e74
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.
15 pages