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pro vyhledávání: '"Bobrova, Irina"'
Autor:
Bobrova, Irina
A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of $A_n^{(1)}$, $n
Externí odkaz:
http://arxiv.org/abs/2403.18463
We have derived a non-abelian analog for the two-dimensional discrete Toda lattice which possesses solutions in terms of quasideterminants and admits Lax pairs of different forms. Its connection with non-abelian analogs for several well-known (1+1) a
Externí odkaz:
http://arxiv.org/abs/2311.11124
Autor:
Bobrova, Irina, Sokolov, Vladimir
We find all non-abelian generalizations of $\text{P}_1 - \text{P}_6$ Painlev\'e systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representation
Externí odkaz:
http://arxiv.org/abs/2303.10347
Autor:
Bobrova, Irina
In this paper, we discuss a connection between different linearizations for non-abelian analogs of the second Painlev\'e equation. For each of the analogs, we listed the pairs of the Harnard-Tracy-Widom (HTW), Flaschka-Newell (FN), and Jimbo-Miwa (JM
Externí odkaz:
http://arxiv.org/abs/2302.10694
Autor:
Bobrova, Irina, Sokolov, Vladimir
All Hamiltonian non-abelian Painlev\'e systems of ${\rm{P}}_{1}-{\rm{P}}_{6}$ type with constant coefficients are found. For ${\rm{P}}_{1}-{\rm{P}}_{5}$ systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To
Externí odkaz:
http://arxiv.org/abs/2209.00258
Autor:
Bobrova, Irina, Sokolov, Vladimir
We study non-abelian systems of Painlev\'e type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in the sense of the existence of a non-abelian first integral that gener
Externí odkaz:
http://arxiv.org/abs/2206.10580
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.
Comment: The formula (54
Comment: The formula (54
Externí odkaz:
http://arxiv.org/abs/2205.05107
Publikováno v:
In Physica D: Nonlinear Phenomena August 2024 464
Autor:
Bobrova, Irina, Sokolov, Vladimir
For all non-equivalent matrix systems of Painlev\'e-4 type found by authors in arXiv:2107.11680, isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlev\'e-2 equations are found.
Externí odkaz:
http://arxiv.org/abs/2110.12159
Autor:
Bobrova, Irina, Mazzocco, Marta
In this paper we study the so-called sigma form of the second Painlev\'e hierarchy. To obtain this form, we use some properties of the Hamiltonian structure of the second Painlev\'e hierarchy and of the Lenard operator.
Externí odkaz:
http://arxiv.org/abs/2012.11010