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arXiv · 2311.11124

Non-Abelian discrete Toda chains and related lattices

Irina Bobrova·Vladimir Retakh·Vladimir Rubtsov·Georgy Sharygin
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Abstract

We have derived a non-abelian analog for the two-dimensional discrete Toda lattice which possesses solutions in terms of quasideterminants and admits Lax pairs of different forms. Its connection with non-abelian analogs for several well-known (1+1) and one-dimensional lattices is discussed. In particular, we consider a non-commutative analog of the scheme: discrete Toda equations $\rightarrow$ Somos-$N$ sequences $\rightarrow$ discrete Painlev\'e equations.

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Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin. 2023-11-18. Non-Abelian discrete Toda chains and related lattices. https://doi.org/10.1016/j.physd.2024.134200

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