论文标题
非共同的HERMITE-PADé近似和集成性
Non-commutative Hermite--Padé approximation and integrability
论文作者
论文摘要
我们介绍并解决了Hermite-Padé类型I近似问题的非交通性版本。它的解决方案由准固定剂表达，以一种自然的方式导致了非交通式Hirota（离散kadomtsev-petviashvili）系统的解决方案及其线性问题。我们还证明了约束系统的整合性，在最简单的情况下，它是从非共同的padé近似值和基质正交多项式的理论中已知的非交换时间TODA晶格方程。
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.
