12 citations · 44 across the 7 of their papers we have counts for
7 papers
On Symmetrizers in Quantum Matrix Algebras
Dmitry Gurevich, Pavel Saponov, Vladimir Sokolov
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions…
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…
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…
Nonlinear waves in two-component Bose-Einstein condensates: Manakov system and Kowalevski equations
A. M. Kamchatnov, V. V. Sokolov
Traveling waves in two-component Bose-Einstein condensates whose dynamics is described by the Manakov limit of the Gross-Pitaevskii equations are considered in general situation wi…