Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation
Vladimir Retakh, Vladimir Rubtsov
TL;DR
This paper develops solutions for noncommutative Toda systems and Painlevé II equations using quasideterminants of Hankel matrices, extending classical integrable systems into the noncommutative setting.
Contribution
It introduces a novel approach to solving noncommutative integrable systems via quasideterminants, bridging Hankel matrices and Painlevé equations.
Findings
Constructed solutions for noncommutative Toda systems.
Extended Painlevé II equations into noncommutative frameworks.
Demonstrated the use of quasideterminants in noncommutative integrable systems.
Abstract
We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.
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