Non-Abelian discrete Toda chains and related lattices

Author:

Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov, Georgy Sharygin

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph), Quantum Algebra (math.QA)

journal:

date:

2023-11-18 00:00:00

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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