Lattice equations arising from discrete Painlevé systems. I. (A2 + A1)(1) and (A1 + A1')(1) cases

Nalini Joshi; Nobutaka Nakazono; Yang Shi

doi:10.1063/1.4931481

Lattice equations arising from discrete Painlevé systems. I. (A₂ + A₁)⁽¹⁾ and (A₁ + A₁^')⁽¹⁾ cases

Nalini Joshi, Nobutaka Nakazono, Yang Shi

Flinders University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the concept of ω-lattice, constructed from τ functions of Painlevé systems, on which quad-equations of ABS (Adler-Bobenko-Suris) type appear. In particular, we consider the A₅⁽¹⁾- and A₆⁽¹⁾-surface q-Painlevé systems corresponding affine Weyl group symmetries are of (A₂ + A₁)⁽¹⁾ and (A₁ + A₁^')⁽¹⁾-types, respectively.

Original language	English
Article number	092705
Number of pages	26
Journal	Journal of Mathematical Physics
Volume	56
Issue number	9
DOIs	https://doi.org/10.1063/1.4931481
Publication status	Published - 30 Sep 2015

Keywords

dynamical systems
Euclidean geometries
complex functions

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abstract = "We introduce the concept of ω-lattice, constructed from τ functions of Painlev{\'e} systems, on which quad-equations of ABS (Adler-Bobenko-Suris) type appear. In particular, we consider the A5(1)- and A6(1)-surface q-Painlev{\'e} systems corresponding affine Weyl group symmetries are of (A2 + A1)(1) and (A1 + A1')(1)-types, respectively.",

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AB - We introduce the concept of ω-lattice, constructed from τ functions of Painlevé systems, on which quad-equations of ABS (Adler-Bobenko-Suris) type appear. In particular, we consider the A5(1)- and A6(1)-surface q-Painlevé systems corresponding affine Weyl group symmetries are of (A2 + A1)(1) and (A1 + A1')(1)-types, respectively.

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Lattice equations arising from discrete Painlevé systems. I. (A₂ + A₁)⁽¹⁾ and (A₁ + A₁^')⁽¹⁾ cases

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