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arXiv · 1704.05403

Co-primeness preserving higher dimensional extension of $q$-discrete Painlev\'e I, II equations

Naoto Okubo
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Abstract

We construct the $q$-discrete Painlev\'{e} 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 Painlev\'{e} 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.

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Naoto Okubo. 2017-04-18. Co-primeness preserving higher dimensional extension of $q$-discrete Painlev\'e I, II equations. https://doi.org/10.46298/ocnmp.15632

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