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math-ph2022★ 7 cited
A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov +1
We study a fully noncommutative generalisation of the commutative fourth Painlevé equation that possesses solutions in terms of an infinite Toda system over an associative unital d…
math-ph2010★ 35 cited
Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation
Vladimir Retakh, Vladimir Rubtsov
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 Hank…