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

Mattia Cafasso (1) , Di Yang

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Domaines: Physique mathématique [math-ph]

Mattia Cafasso, Di Yang. Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method. 2021. ⟨hal-03505377⟩