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arxiv: 1308.5018 · v3 · pith:N3B22X3Anew · submitted 2013-08-22 · 🌊 nlin.SI · math-ph· math.MP

On some classes of discrete polynomials and ordinary difference equations

Andrei K. Svinin This is my paper
classification 🌊 nlin.SI math-phmath.MP
keywords discretepolynomialsclassesconstructequationssomeadmittingallows
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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.

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  1. A non-commutative discrete first Painlev\'e hierarchy: the Lax pair approach

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    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 ...