A fully noncommutative analog of the Painlev\'e IV equation and a structure of its solutions
Irina Bobrova, Vladimir Retakh, Vladimir Rubtsov, and Georgy Sharygin
TL;DR
This paper introduces a noncommutative generalization of the Painlevé IV equation, exploring its solutions within an infinite Toda system over a division ring, expanding the understanding of integrable systems in noncommutative settings.
Contribution
It presents the first fully noncommutative analog of Painlevé IV and analyzes its solution structure using an infinite Toda system over a division ring.
Findings
Established a noncommutative Painlevé IV equation
Linked solutions to an infinite Toda system
Extended integrable systems theory to noncommutative algebra
Abstract
We study a fully noncommutative generalisation of the commutative fourth Painlev\'e equation that possesses solutions in terms of an infinite Toda system over an associative unital division ring equipped by a derivation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra · Algebraic structures and combinatorial models