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
On some classes of discrete polynomials and ordinary difference equations
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abstract
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its explicit form and show some examples.
fields
nlin.SI 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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