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Тау-функция иерархии Тоды типа B
Теоретическая и математическая физика. 2023. Т. 217. № 2. С. 299–316.
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B), which can be regarded as a discretization of the BKP hierarchy. We introduce the tau function of the B-Toda hierarchy and obtain bilinear equations for it. Examples of soliton tau functions are presented in explicit form.
Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.
We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...
Added: September 28, 2026
Guterman A., Jonoska N., Kreines E. et al., Proceedings of the Edinburgh Mathematical Society 2026 Vol. 69 No. 3 P. 1041–1057
We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative to its size. These conditions serve to prove the conjecture that such a maximum, which is equal to 𝐹_(2𝑛+1) −1, ...
Added: September 27, 2026
Shishkina E., Современная математика. Фундаментальные направления 2026 Т. 72 № 1 С. 52–67
In this paper, we construct a weighted Sobolev space of fractional order based on the
generalized Bessel potential.We apply these results to the analysis of the singular fractional Schr¨odinger
equation. To solve the Cauchy problem for this equation, we prove an estimate that relates the norm of
the solution to the norm of the initial condition in the ...
Added: September 26, 2026
Shishkina E., Computational Mathematics and Mathematical Physics 2026 Vol. 66 No. 5 P. 804–815
This article demonstrates that the Laplace–Bessel operator generates a strongly continuous
semigroup on a weighted Lebesgue space. Using this semigroup, we define the fractional Laplace–
Bessel operator via Balakrishnan’s formula. Furthermore, we derive three distinct representations for
fractional powers of the negative Laplace–Bessel operator. ...
Added: September 26, 2026
Kolokoltsov V., Shishkina E., Journal of Theoretical Probability 2026 P. 39–83
In this paper, we introduce a new construction of fractional derivatives and integrals
with respect to a function, based on a matrix approach. We believe that this is a powerful
tool in both analytical and numerical calculations.We begin with the differential
operator with respect to a function that generates a semigroup. By discretizing this
operator, we obtain a matrix ...
Added: September 26, 2026
Petr Kucheriaviy, Bulletin of the Australian Mathematical Society 2026
We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. ...
Added: September 25, 2026
Пелевин Ф. Е., Математические заметки 2026 Т. 120 № 1 С. 159–163
Две не равные тождественно нулю функции (последовательности элементов некоторого поля) будем называть эквивалентными, если они удовлетворяют функциональному уравнению типа теорем сложения тэта-функций. Основной результат работы состоит в том, что рассматриваемое отношение действительно является отношением эквивалентности. ...
Added: September 25, 2026
Shimanogov I. N., Vyalyi M., Siberian Mathematical Journal 2026 Vol. 67 No. 5 P. 1203–1212
We consider a class of Boolean algebras formed by intersections of regular languages with
a given language. In the case where such an algebra is isomorphic to the algebra of regular languages,
we prove the existence of an isomorphism that is computable using oracles for the regular realizability
problem and the infinite regular realizability problem. This result yields ...
Added: September 25, 2026
Ramazanov I., Bukh A., Shepelev Igor A., Chaos 2026 No. 36 P. 083150–083150
We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh–Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial ...
Added: September 24, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Sokolov V., Adler V. E., Journal of Geometry and Physics 2026 Vol. 227 Article 105860
The group reduction procedure is applied to vector generalizations of the NLS, mKdV,
and KdV equations. The resulting ODE systems admit isomonodromic Lax representations
and are multicomponent generalizations of the Painlevé equations P 1, P 2, P 34, and P 4.
Some of them can be interpreted as nonautonomous deformations of well-known systems
integrable in the Liouville sense, in ...
Added: September 24, 2026
Sokolov V., BALAKHNEV M. Y., Ufa Mathematical Journal 2026 Vol. 18 No. №3 P. 85–93
A collection of miscellaneous continuous, semi-discrete, and discrete integrable
systems can be associated with each integrable evolution equation of the KdV type. We provide them for the Schwarz — KdV equation and generalize to the vector case. The existence
of these vector generalizations is a non-trivial found fact, no mathematical explanation of
which is known yet. ...
Added: September 24, 2026
Yakovlev E., Maksimov D. A., Mathematical notes 2026 Vol. 120 No. 3 P. 483–496
Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
Added: September 24, 2026
Sokolov V., Shabat G. B., Tsiganov A. V., Journal of Geometry and Physics 2026 Vol. 220
We consider Novikov equations for commutative ring generated by differential operators of
orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method
of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve
of genus 2 for the Novikov equations ...
Added: September 24, 2026
Marshakov A., Yung A., Ievlev E. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 No. 114 P. 1–22
We continue the study of non-Abelian vortex string in 4D N ¼ 2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf ¼ 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by ...
Added: September 24, 2026
Demina M.V., Nechitailo V., Analysis and Mathematical Physics 2026 Vol. 16 No. 5 P. 1–25
We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property R-integrable. These invariants are not necessarily polynomial; they can ...
Added: September 24, 2026
Bitter I., Konakov V., Mathematical notes 2026 Vol. 120 No. 4 P. 599–615
The paper provides a generalization of the local limit theorem on the convergence
of inhomogeneous Markov chains to the diffusion limit for the case in which the corresponding
coefficients of the process satisfy weak regularity conditions and coincide only asymptotically.
In particular, the drift coefficients under consideration can be unbounded with at most linear
growth, and the bounds reflect ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Prokofev V., Zabrodin A., Theoretical and Mathematical Physics 2021 Vol. 208 P. 1093–115
We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions of the zeroth time t_0=x. It is known that their poles as functions of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal of this paper is to extend this correspondence to the level of hierarchies. We show that the ...
Added: July 14, 2026
Beklaryan A., Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 11 P. 2588–2610
This paper is a continuation of the work by L.A. Belkaryan and A.L. Belkaryan published in this journal (64 (7), 1472–1490 (2024)). A theorem is proved formulated as a conjecture in the preceding paper stating the existence and uniqueness of soliton solutions and corresponding solutions of the functional differential equation from a dual pair “function–operator.” For ...
Added: January 27, 2025
Beklaryan L. A., A. L. Beklaryan, Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 7 P. 1472–1490
The dualism of the theories of soliton solutions and solutions to functional differential equations of pointwise type is discussed. We describe the foundations underlying the formalism of this dualism, the central element of which is the concept of a soliton bouquet, as well as a dual pair “function–operator.” Within the framework of this approach, it is possible ...
Added: September 11, 2024
Бекларян Л. А., Beklaryan A., В кн.: Современные методы теории функций и смежные проблемы: материалы Международной конференции "Воронежская зимняя математическая школа".: Воронеж: Издательский дом ВГУ, 2023. С. 54–57.
Added: June 5, 2023
Beklaryan A., Бекларян Л. А., Журнал вычислительной математики и математической физики 2022 Т. 62 № 6 С. 933–950
The existence of a family of bounded soliton solutions for a finite-difference analogue of the wave equation with a general nonlinear potential is proved. The proof is based on a formalism establishing a one-to-one correspondence between soliton solutions of an infinite-dimensional dynamical system and solutions of a family of functional differential equations of the pointwise type. A key ...
Added: May 30, 2022
Beklaryan L. A., Beklaryan A., Computational Mathematics and Mathematical Physics 2021 Vol. 61 No. 12 P. 1980–1994
The existence of a family of bounded soliton solutions for a finite-difference wave equation with a quadratic potential is established. The proof is based on a formalism establishing a one-to-one correspondence between the soliton solutions of an infinite-dimensional dynamical system and the solutions of a family of functional differential equations of the pointwise type. A ...
Added: January 14, 2022