12 citations · 41 across the 8 of their papers we have counts for
8 papers
A non-commutative discrete first Painlevé hierarchy: the Lax pair approach
Irina Bobrova
Using a non-commutative analogue of the isomonodromic problem associated with the discrete first Painlevé hierarchy, we construct a non-commutative version of this hierarchy, denot…
On classification of non-abelian Painlevé type systems
Irina Bobrova, Vladimir Sokolov
We find all non-abelian generalizations of Painlevé systems such that the corresponding autonomous system obtained by freezing the independent variable is…
Classification of Hamiltonian non-abelian Painlevé type systems
Irina Bobrova, Vladimir Sokolov
All Hamiltonian non-abelian Painlevé systems of type with constant coefficients are found. For systems, we replace an approp…
Non-abelian Painlevé systems with generalized Okamoto integral
Irina Bobrova, Vladimir Sokolov
We study non-abelian systems of Painlevé type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in t…
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…
On matrix Painlevé-4 equations. Part 2: Isomonodromic Lax pairs
Irina Bobrova, Vladimir Sokolov
For all non-equivalent matrix systems of Painlevé-4 type found by authors in arXiv:2107.11680, isomonodromic Lax pairs are presented. Limiting transitions from these systems to mat…
On matrix Painlevé-4 equations. Part 1: Painlevé--Kovalevskaya test
Irina Bobrova, Vladimir Sokolov
Using the Painlevé--Kovalevskaya test, we find several new matrix generalizations of the Painlevé-4 equation. Some limiting transitions reduce them to known matrix Painlevé-2 equat…
The Sigma Form for the PII Hierarchy
Irina Bobrova, Marta Mazzocco
In this paper we study the so-called sigma form of the second Painlevé hierarchy. To obtain this form, we use some properties of the Hamiltonian structure of the second Painlevé hi…