Non-commutative Hermite--Padé approximation and integrability

Abstract

We introduce and solve the non-commutative version of the Hermite-Padé type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subclass of solutions of the non-commutative Hirota (discrete Kadomtsev--Petviashvili) system and of its linear problem. We also prove integrability of the constrained system, which in the simplest case is the non-commutative discrete-time Toda lattice equation known from the theory of non-commutative Padé approximants and matrix orthogonal polynomials.

10 pages

References in corpus (4)

• Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
• Noncommutative integrability, paths and quasi-determinants
• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits

Cited by in corpus (2)

• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Non-autonomous multidimensional Toda system and multiple interpolation problem