On non-commutative leapfrog map

2023/10/03 by Bao Wang, Wang, Bao, Shi‐Hao Li +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2310.01993

openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the integrability of the non-commutative leapfrog map in this paper. Firstly, we derive the explicit formula for the non-commutative leapfrog map and corresponding discrete zero-curvature equation by employing the concept of non-commutative cross-ratio. Then we revisit this discrete map, as well as its continuous limit, from the perspective of non-commutative Laurent bi-orthogonal polynomials. Finally, the Poisson structure for this discrete non-commutative map is formulated with the help of a non-commutative network. We aim to enhance our understanding of the integrability properties of the non-commutative leapfrog map and its related mathematical structures through these analysis and constructions.

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• Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
• Integrable pentagram-type maps on polyhedra via partial difference operators

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