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arXiv · 2112.14202

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

Mattia Cafasso·Di Yang
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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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Mattia Cafasso, Di Yang. 2021-12-28. Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method. https://doi.org/10.1088/1751-8121%2Fac5e74

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