Discrete Lax pairs and hierarchies of integrable difference systems

2021/04/29 by Pavlos Kassotakis, Kassotakis, Pavlos
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons #msc:37K10 #msc:37K60 #msc:39A14 #nlin.SI

paper · pdf · doi:10.48550/arxiv.2104.14529

27 pages

arxiv created 2021/04/29 · arxiv updated 2021/04/30

Abstract

We introduce a family of order N∈ ℕ Lax matrices that is indexed by the natural number k∈ \1,…,N-1\. For each value of k they serve as strong Lax matrices of a hierarchy of integrable difference systems in edge variables that in turn lead to hierarchies of integrable difference systems in vertex variables or in a combination of edge and vertex variables. Furthermore, the entries of the Lax matrices are considered as elements of a division ring, so we obtain hierarchies of discrete integrable systems extended in the non-commutative domain.

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