Lax pairs of discrete Painlev\'e equations: $(A_2+A_1)^{(1)}$ case

Nalini Joshi; Nobutaka Nakazono

arxiv: 1503.04515 · v5 · pith:IIBWAGQEnew · submitted 2015-03-16 · 🧮 math-ph · math.MP· nlin.SI

Lax pairs of discrete Painlev\'e equations: (A₂+A₁)⁽¹⁾ case

Nalini Joshi , Nobutaka Nakazono This is my paper

classification 🧮 math-ph math.MPnlin.SI

keywords painlevpairsdiscreteequationsaffinecasecomprehensiveconsider

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In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlev\'e equations by using a reduced hypercube structure. In particular, we consider the $A_5^{(1)}$-surface $q$-Painlev\'e system which has the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$. Two new Lax pairs are found.

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Lax pairs of discrete Painlev\'e equations: (A₂+A₁)⁽¹⁾ case

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