Tau-functions for the Ablowitz–Ladik hierarchy: the matrix-resolvent method
- 20 April 2022
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (20), 204001
- https://doi.org/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.Funding Information
- CNRS (International Research Project PIICQ)
- IPaDEGAN (H2020-MSCA-RISE-2017 PROJECT No. 778010)
- National Key R and D Program of China (2020YFA0713100)
- National Natural Science Foundation of China (12061131014)
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