Year: 2024
Type: article
Abstract: We investigate the integrability of the noncommutative leapfrog map in this paper. First, we derive the explicit formula for the noncommutative leapfrog map and corresponding discrete zero‐curvature equation by employing the concept of noncommutative cross‐ratio. Then we revisit this discrete map, as well as its continuous limit, from the perspective of noncommutative Laurent bi‐orthogonal polynomials. Finally, the Poisson structure for this discrete noncommutative map is formulated with the help of a noncommutative network. Through these constructions, we aim to enhance our understanding of the integrability properties of the noncommutative leapfrog map and its related mathematical structures.
DOI: 10.1112/jlms.70063
Authors: Bao Wang, Shi‐Hao Li
Institutions: Ningbo University, Sichuan University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4405736501