Co-primeness preserving higher dimensional extension of $q$-discrete Painlevé I, II equations

Open Communications in Nonlinear Mathematical Physics 2026 Open access

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Authors: Naoto Okubo
DOI: 10.46298/ocnmp.15632
Cited by: 2

Abstract

We construct the $q$-discrete Painlevé I and II equations and their higher order analogues by virtue of periodic cluster algebras. Using particular $k \times k$ exchange matrices, we show that the cluster algebras corresponding to $k=4$ and $5$ give the $q$-discrete Painlevé I and II equations respectively. For $k \ge 6$, we obtain higher-order discrete equations that satisfy an integrability criterion, namely, the co-primeness property.

Fields of Study & Subjects

Nonlinear Waves and Solitons Algebraic structures and combinatorial models Advanced Topics in Algebra

Publication details

Journal / source
Open Communications in Nonlinear Mathematical Physics
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Volume
Volume 6
Publication date
18 August 2026
Language
EN