On some classes of discrete polynomials and ordinary difference equations

2013/08/31 by Andrei K. Svinin, Andrei K Svinin · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Class (philosophy) #Construct (python library) #Discrete orthogonal polynomials #Integrable system #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Orthogonal polynomials #Polynomial and algebraic computation #Representation (politics) #Wilson polynomials #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/1751-8113/47/15/155201

published as J. Phys. A: Math. Theor. V.47 (2014) Art. No.155201 · LaTex

arxiv created 2014/03/24 · openalex publication_date 2014/03/28 · arxiv updated 2014/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We introduce two classes of discrete polynomials and use them to construct ordinary difference equations admitting a Lax representation in terms of these polynomials. We also construct lattice integrable hierarchies in their explicit form and show some examples.

Cited by

• Invariants for a family of discrete equations with the Laurent property
• A non-commutative discrete first Painlevé hierarchy: the Lax pair approach

Related

• On integrals for some class of ordinary difference equations admitting a Lax pair representation
• On some class of homogeneous polynomials and explicit form of integrable hierarchies of differential-difference equations
• A completeness study on a class of discrete, 'two by two' Lax pairs
• Discrete Lax pairs and hierarchies of integrable difference systems
• ℤ_N graded discrete Lax pairs and Yang-Baxter maps