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

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03505377
Contributor : Mattia Cafasso Connect in order to contact the contributor
Submitted on : Thursday, December 30, 2021 - 4:55:14 PM
Last modification on : Sunday, June 26, 2022 - 3:29:37 AM

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  • HAL Id : hal-03505377, version 1
  • ARXIV : 2112.14202

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

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