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Vladimir Sokolov

Publications and source records attributed to Vladimir Sokolov.

At least 19 recordsLinked to original sources
arXiv2025

Thermodynamics of charged black points in vacuum nonlinear electrodynamics

The paper analyzes the thermodynamic properties of a special state of charged black holes, in which the event horizon becomes point-like and coincides with the singularity. It is shown that for such states, called black points, in contrast to Reissner-Nordström black holes, the third law of thermodynamics in Planck's formulation is fulfilled. It is also shown that the formation of a black point is not a first-order phase transition. Considerable attention is paid to the special state of a black point with a doubly degenerate horizon, similar to the extreme state of a Reissner-Nordström black hole.

gr-qc↗
arXiv2025

Extreme black points in Born-Infeld electrodynamics

The article considers the space-time structure of a charged black hole in the nonlinear Born-Infeld electrodynamics. We are discussing a special state of such a black hole in the form of a "black point" with a doubly degenerate horizon, for which the pseudo-Riemannian spacetime has a timelike singularity, and the effective space-time for photons turns out to be everywhere regular. This property makes extreme black points an intermediate state between traditional and absolutely regular black holes.

gr-qc↗
arXiv2024

Integrability conditions for Boussinesq type systems

The symmetry approach to the classification of evolution integrable partial differential equations (see, for example \cite{MikShaSok91}) produces an infinite series of functions, defined in terms of the right hand side, that are conserved densities of any equation having infinitely many infinitesimal symmetries. For instance, the function $\frac{\partial f}{\partial u_{x}}$ has to be a conserved density of any integrable equation of the KdV type $u_t=u_{xxx}+f(u,u_x)$. This fact imposes very strong conditions on the form of the function $f$. In this paper we construct similar canonical densities for equations of the Boussinesq type. In order to do that, we write the equations as evolution systems and generalise the formal diagonalisation procedure proposed in \cite{MSY} to these systems.

nlin.SI↗
arXiv2023

Classification of Hamiltonian non-abelian Painlevé type systems

All Hamiltonian non-abelian Painlevé 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 prove the integrability of new ${\rm{P}}_{3}^{\prime}$ and ${\rm{P}}_{5}$ systems thus obtained, we find isomonodromic Lax pairs for them.

nlin.SI↗
arXiv2023

On Symmetrizers in Quantum Matrix Algebras

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 classical Lie groups (the RTT algebras). We consider the problem of constructing some projectors on homogenous components of such algebras, which are analogs of the usual symmetrizers. The main objective of this note is to present a method, which hopefully enables one to construct symmetrizers on all homogenous components of the RTT algebras. We illustrate the construction by two low-dimensional examples. A way of extending this method onto other quantum matrix algebras is also discussed.

math.QA↗
arXiv2023

On classification of non-abelian Painlevé type systems

We find all non-abelian generalizations of $\text{P}_1 - \text{P}_6$ Painlevé systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representations.

nlin.SI↗
arXiv2023

Comparison of Optical and Electrical Links for Highly-Interconnected Systems

As data rates for multi-gigabit serial interfaces within multi-node compute systems approach and exceed 10 Gigabits per second (Gbps), board-to-board and chip-to-chip optical signaling solutions become more attractive, particularly for longer (e.g. 50-100 cm) links. The transition to optical signaling will potentially allow new high performance compute (HPC) system architectures that benefit from characteristics unique to optical links. To examine these characteristics, we built and tested several optical demonstration vehicles; one based on dense wavelength division multiplexing (DWDM), and others based on multiple point-to-point links carried across multimode fibers. All test vehicles were constructed to evaluate applicability to a multi-node compute system. Test results, combined with data from recent research efforts are summarized and compared to equivalent electrical links and the advantages and design characteristics unique to optical signaling are identified.

eess.SP↗
arXiv2022

Non-abelian Painlevé systems with generalized Okamoto integral

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 the sense of the existence of a non-abelian first integral that generalizes the Okamoto Hamiltonian. All non-abelian P6-P2-systems with such integrals are found. A coalescence limiting scheme is constructed for these non-abelian Painlevé systems. This allows us to construct an isomonodromic Lax pair for each of them.

nlin.SI↗
arXiv2019

The symmetry approach to integrability: recent advances

We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further describe non-abelian integrable equations, especially matrix (ODE and PDE) systems. Some non-evolutionary integrable equations are studied using a formulation of formal recursion operators that allows to study non-diagonalisable systems of evolution equations.

nlin.SI↗
arXiv2017

Symmetry approach to integrability and non-associative algebraic structures

The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand side are considered. Such systems are associated with associative algebras and, more generally, with non-associative algebraic structures, whose structural constants are defined by the coefficients of the system under consideration. We explore which structures correspond to polynomial integrable models. Integrable systems polynomial in derivatives are described in geometric terms. The third part we consider integrable vector izotropic and anizotropic systems.

nlin.SI↗
arXiv2017

Algebraic structures related to integrable differential equations

The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a complementary subalgebra. Examples of complementary subalgebras and corresponding integrable models are presented. In the framework of the bi-Hamiltonian approach compatible associative algebras related affine Dynkin diagrams are considered. A bi-Hamiltonian origin of the classical elliptic Calogero-Moser models is revealed.

nlin.SI↗
arXiv2015

Algebraic quantum Hamiltonians on the plane

We consider second order differential operators $P$ with polynomial coefficients that preserve the vector space $V_k$ of polynomials of degrees not greater then $k$. We assume that the metric associated with the symbol of $P$ is flat and that the operator $P$ is potential. In the case of two independent variables we obtain some classification results and find polynomial forms for the elliptic $A_2$ and $G_2$ Calogero-Moser Hamiltonians and for the elliptic Inosemtsev model.

nlin.SI↗
arXiv2013

Parameter-dependent associative Yang-Baxter equations and Poisson brackets

We discuss associative analogues of classical Yang-Baxter equation meromorphically dependent on parameters. We discover that such equations enter in a description of a general class of parameter-dependent Poisson structures and double Lie and Poisson structures in sense of M. Van den Bergh. We propose a classification of all solutions for one-dimensional associative Yang-Baxter equations.

math-ph↗
arXiv2013

Vector hyperbolic equations on the sphere possessing integrable third order symmetries

The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we mean the existence of vector Backlund transformations depending on a parameter. For all new equations such transformations are constructed.

nlin.SI↗
arXiv2011

Single-Crystal and Powder Neutron Diffraction Study of FeXMn1-XS Solid Solutions

FeXMn1-XS (0 <x< 0.3) synthesized on the basis of α-MnS are the novel Mott-type substances with the rock salt structure. Neutron diffraction study shows that the shift of the Neel temperature of these materials from 150 (x = 0) to 200 K (x = 0.29) under the action of chemical pressure (x) is accompanied by a decrease in the cubic NaCl lattice parameters. The structural transition with a change in crystal symmetry and a decrease in resistance before the magnetic transition at x = 0.25 is found. Therefore, FeXMn1-XS are interesting materials for both fundamental study of the interrelation between the magnetic, electrical, and structural properties in systems with the strong electron correlations of a MnO-type and application.

cond-mat.mtrl-sci↗
arXiv2011

Bi-Hamiltonian ODEs with matrix variables

We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets and found the corresponding hierarchy of integrable models, which generalizes the two-component Manakov's matrix system in the case of arbitrary number of matrices.

nlin.SI↗