Discrete Lax pairs and hierarchies of integrable difference systems

Abstract

We introduce a family of order $N\in \mathbb{N}$ Lax matrices that is indexed by the natural number $k\in \{1,\dots ,N-1\}.$ 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.

arXiv comment27 pages

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Cited by in corpus (3)

• On non-abelian quadrirational Yang-Baxter maps
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps