Constructs non-commutative discrete first Painlevé hierarchy d-PI_m^nc via non-commutative isomonodromic problem, expresses both commutative and non-commutative versions via Svinin polynomials, derives reduction from non-commutative Volterra lattice, and gives continuous limits for first three membe
Non-commutative q-Painleve VI equation
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abstract
By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI equation with full range of parameters as the (2,2) similarity reduction of the non-commutative, non-isospectral and non-autonomous lattice modified Korteweg-de Vries equation. We also comment on the fact that in making the analogous reduction starting from Schwarzian Korteweg-de Vries equation no such "non-isospectral generalization" is needed.
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2026 1verdicts
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A non-commutative discrete first Painlev\'e hierarchy: the Lax pair approach
Constructs non-commutative discrete first Painlevé hierarchy d-PI_m^nc via non-commutative isomonodromic problem, expresses both commutative and non-commutative versions via Svinin polynomials, derives reduction from non-commutative Volterra lattice, and gives continuous limits for first three membe