Variations of $q$-Garnier system
Hidehito Nagao, Yasuhiko Yamada
TL;DR
This paper explores different variants of the q-Garnier system related to discrete time evolutions and examines their connection to Suzuki's higher order q-Painlevé system through a duality in the q-KP framework.
Contribution
It introduces new variants of the q-Garnier system and establishes a link to Suzuki's higher order q-Painlevé system using duality principles.
Findings
Identified multiple variants of the q-Garnier system.
Established a relation between q-Garnier and higher order q-Painlevé systems.
Utilized duality of the q-KP system to connect different integrable systems.
Abstract
We study several variants of q-Garnier system corresponding to various directions of discrete time evolutions. We also investigate a relation between the -Garnier system and Suzuki's higher order -Painlev/'e system by using a duality of the -KP system.
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