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Evolution of flat perturbations in a cosmological environment of a scalar field with self-action and an ideal scalar-neutral fluid 具有自作用的标量场和理想标量中性流体的宇宙学环境中平坦微扰的演化
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020091
Yu. G. Ignat’ev
{"title":"Evolution of flat perturbations in a cosmological environment of a scalar field with self-action and an ideal scalar-neutral fluid","authors":"Yu. G. Ignat’ev","doi":"10.1134/S0040577926020091","DOIUrl":"10.1134/S0040577926020091","url":null,"abstract":"<p> We formulate and investigate a mathematical model of the <span>(mathbf{S^{(0)}})</span> cosmological system based on a classical scalar field with self-interaction and an ideal scalar-neutral fluid. For a nonzero fluid energy density, the system of equations for the perturbations is reduced to a Lifshitz–Khalatnikov form, which is used to study the cosmological evolution of perturbations at singular points of the <span>(mathbf{S^{(0)}})</span> background model. At these points, the scalar field, on the one hand, and the gravitational perturbations and the fluid, on the other, become independent subsystems. We find exact solutions for the perturbations of the scalar field, gravitational perturbations, and the perturbation of the energy-momentum of the fluid for its nonrelativistic and ultrarelativistic states. Near stable singular points of the background, the perturbations decay, while near unstable singular points, they grow exponentially rapidly. We find an asymptotic solution to the equation for the perturbation of a scalar field for sufficiently large wavenumbers. This solution is used to establish necessary and sufficient conditions for system instability and evolution. We establish laws for scaling the results of perturbation theory to the parameters of known field-theoretical interaction models. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"338 - 371"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the constructive solvability of a class of nonlinear multidimensional integral equations in the theory of (p)-adic strings (p) -进弦理论中一类非线性多维积分方程的构造可解性
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020078
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan
{"title":"On the constructive solvability of a class of nonlinear multidimensional integral equations in the theory of (p)-adic strings","authors":"A. Kh. Khachatryan,&nbsp;Kh. A. Khachatryan,&nbsp;H. S. Petrosyan","doi":"10.1134/S0040577926020078","DOIUrl":"10.1134/S0040577926020078","url":null,"abstract":"<p> We study multidimensional integral equations with monotonic and odd nonlinearity. These equations have applications in the dynamic theory of <span>(p)</span>-adic strings. In particular, when the nonlinearity is power-law and the kernels are represented as Gaussian distributions, these equations describe the dynamics (rolling) of <span>(p)</span>-adic open or open–closed strings for a scalar tachyon field. Under certain restrictions on nonlinearity and kernels, we prove the constructive solvability of the equation in the space of continuous and bounded functions. We establish the uniform convergence of the corresponding successive approximations (with a rate of infinitely decreasing geometric progression) to the solution. We prove that the equation under study can simultaneously have alternating and sign-preserving bounded solutions. The results obtained are applied to specific problems in the dynamic theory of <span>(p)</span>-adic strings and in solving a nonlinear boundary value problem for the heat conduction equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"298 - 312"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effects of changing the multiplicity of terms in the Cauchy problem for the Dirac equation in graphene with a constant electric field and a localized initial condition 恒定电场和定域初始条件下石墨烯中Dirac方程Cauchy问题项数变化的影响
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020030
I. A. Bogaevskii, S. Yu. Dobrokhotov, A. A. Tolchennikov
{"title":"Effects of changing the multiplicity of terms in the Cauchy problem for the Dirac equation in graphene with a constant electric field and a localized initial condition","authors":"I. A. Bogaevskii,&nbsp;S. Yu. Dobrokhotov,&nbsp;A. A. Tolchennikov","doi":"10.1134/S0040577926020030","DOIUrl":"10.1134/S0040577926020030","url":null,"abstract":"<p> We consider the Cauchy problem for the two-dimensional massless Dirac equation in graphene with a constant electric field. It is assumed that at the initial time, a localized wave function describes quasi-electrons with momenta lying in the right half-plane. We describe the effect based on the phenomenon of changing the multiplicity of terms (characteristics), which leads to Klein tunneling and consists in the fact that, after some time, a hole component appears in addition to the wave function for the electron component. The components move in opposite directions, and the hole component localizes near a moving point. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"217 - 235"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The three-component coupled time-varying coefficient complex mKdV equation via the (bar{partial})-dressing method 通过(bar{partial}) -修整法得到三分量耦合时变系数复mKdV方程
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020066
Tao Deng, Qi Chen, Chunxia Li
{"title":"The three-component coupled time-varying coefficient complex mKdV equation via the (bar{partial})-dressing method","authors":"Tao Deng,&nbsp;Qi Chen,&nbsp;Chunxia Li","doi":"10.1134/S0040577926020066","DOIUrl":"10.1134/S0040577926020066","url":null,"abstract":"<p> In this paper we focus on the application of the <span>(bar{partial})</span>-dressing method to the three-component coupled time-varying coefficient complex mKdV equation. Based upon a <span>((4 times 4))</span>-matrix <span>(bar{partial})</span>-problem and two linear equations of the spectral transformation matrix, we derive the Lax pair and infinitely many conservation laws for the three-component coupled time-varying coefficient complex mKdV equation. Besides, we construct a hierarchy of the three-component coupled time-varying coefficient complex mKdV equation with a source term by making use of the recursion operator. We derive symmetry conditions of the spectral transformation matrix. We establish <span>(N)</span>-solution solutions and multi-pole solutions for the three-component coupled time-varying coefficient complex mKdV equation and express them in compact forms based on an explicit spectral transformation matrix. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"284 - 297"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-dimensional Riemann–Hilbert problem for commutative monodromy on an elliptic curve 椭圆曲线上可交换单态的二维Riemann-Hilbert问题
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020017
A. M. Nefedova
{"title":"Two-dimensional Riemann–Hilbert problem for commutative monodromy on an elliptic curve","authors":"A. M. Nefedova","doi":"10.1134/S0040577926020017","DOIUrl":"10.1134/S0040577926020017","url":null,"abstract":"<p> We obtain an explicit solution of the Riemann–Hilbert problem on an elliptic curve for the two-dimensional commutative monodromy representations. By an arbitrary set of points together with a representation of the fundamental group of the curve punctured at these points, we construct a semistable holomorphic vector bundle of degree zero with a logarithmic connection possessing the required singularities and monodromy. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"177 - 188"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical elliptic ({rm BC}_1) Ruijsenaars–van Diejen model: relation to Zhukovsky–Volterra gyrostat and 1-site classical (XYZ) model with boundaries 经典椭圆型({rm BC}_1) rujsenaars - van Diejen模型：与Zhukovsky-Volterra陀螺的关系及带边界的1点经典(XYZ)模型
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020029
A. M. Mostovskii, A. V. Zotov
{"title":"Classical elliptic ({rm BC}_1) Ruijsenaars–van Diejen model: relation to Zhukovsky–Volterra gyrostat and 1-site classical (XYZ) model with boundaries","authors":"A. M. Mostovskii,&nbsp;A. V. Zotov","doi":"10.1134/S0040577926020029","DOIUrl":"10.1134/S0040577926020029","url":null,"abstract":"<p> We present a description of the classical elliptic <span>({rm BC}_1)</span> Ruijsenaars–van Diejen model with eight independent coupling constants through a pair of <span>({rm BC}_1)</span> type classical Sklyanin algebras generated by the (classical) quadratic reflection equation with non-dynamical <span>(XYZ)</span> <span>(r)</span>-matrix. For this purpose, we consider the classical version of the <span>(L)</span>-operator for the Ruijsenaars–van Diejen model proposed by O. Chalykh. In the <span>({rm BC}_1)</span> case, it is factorized into the product of two Lax matrices depending on four constants. Then we apply an IRF-Vertex type gauge transformation and obtain a product of the Lax matrices for the Zhukovsky–Volterra gyrostats. Each of them is described by the <span>({rm BC}_1)</span> version of the classical Sklyanin algebra. In particular case, when four pairs of constants coincide, the <span>({rm BC}_1)</span> Ruijsenaars–van Diejen model exactly coincides with the relativistic Zhukovsky–Volterra gyrostat. Explicit change of variables is obtained. We also consider another special case of the <span>({rm BC}_1)</span> Ruijsenaars–van Diejen model with seven independent constants. We show that it can be reproduced by considering the transfer matrix of the classical <span>(1)</span>-site <span>(XYZ)</span> chain with boundaries. In the end of the paper, using another gauge transformation, we represent Chalykh’s Lax matrix in a form depending on Sklyanin’s generators. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"189 - 216"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complex binomial theorem and pentagon identities 复二项式定理与五边形恒等式
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S0040577926010010
N. M. Belousov, G. A. Sarkissian, V. P. Spiridonov
{"title":"Complex binomial theorem and pentagon identities","authors":"N. M. Belousov,&nbsp;G. A. Sarkissian,&nbsp;V. P. Spiridonov","doi":"10.1134/S0040577926010010","DOIUrl":"10.1134/S0040577926010010","url":null,"abstract":"<p> We consider various pentagon identities realized by hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields the complex binomial theorem, which coincides with the Fourier transformation of the complex Euler beta integral evaluation. At the bottom, we obtain a Fourier transformation formula for the complex gamma function. This is done with the help of a new type of the limit <span>(omega_1+omega_2to 0)</span> (or <span>(bto i)</span> in two-dimensional conformal field theory) applied to hyperbolic hypergeometric integrals. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 1","pages":"1 - 20"},"PeriodicalIF":1.1,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zeros of the spatially three-dimensional Pauli–Jordan–Dirac function on spatial intervals 空间区间上空间三维Pauli-Jordan-Dirac函数的零点
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S0040577926010034
E. A. Karatsuba
{"title":"Zeros of the spatially three-dimensional Pauli–Jordan–Dirac function on spatial intervals","authors":"E. A. Karatsuba","doi":"10.1134/S0040577926010034","DOIUrl":"10.1134/S0040577926010034","url":null,"abstract":"<p> We investigate the properties of the Pauli–Jordan–Dirac anticommutator of the quantum field theory of free Dirac electrons in a discrete representation in Minkowski space. We present a method for estimating the number of zeros of the anticommutator on spatial intervals. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 1","pages":"66 - 76"},"PeriodicalIF":1.1,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transformation of the Lax representation of chiral-type systems 手性型系统Lax表示的变换
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S0040577926010046
A. V. Balandin
{"title":"Transformation of the Lax representation of chiral-type systems","authors":"A. V. Balandin","doi":"10.1134/S0040577926010046","DOIUrl":"10.1134/S0040577926010046","url":null,"abstract":"<p> A transformation of the Lax representation of chiral-type systems is obtained. Under some additional conditions, this transformation leads to the Lax representation of a new chiral-type system. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 1","pages":"77 - 86"},"PeriodicalIF":1.1,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analogue of Goeritz matrices for computation of bipartite HOMFLY–PT polynomials 计算二部HOMFLY-PT多项式的Goeritz矩阵的模拟
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S0040577926010022
A. S. Anokhina, D. V. Korzun, E. N. Lanina, A. Yu. Morozov
{"title":"Analogue of Goeritz matrices for computation of bipartite HOMFLY–PT polynomials","authors":"A. S. Anokhina,&nbsp;D. V. Korzun,&nbsp;E. N. Lanina,&nbsp;A. Yu. Morozov","doi":"10.1134/S0040577926010022","DOIUrl":"10.1134/S0040577926010022","url":null,"abstract":"<p> The Goeritz matrix is an alternative to the Kauffman bracket and, in addition, makes it possible to calculate the Jones polynomial faster with some minimal choice of a checkerboard surface of a link diagram. We introduce a modification of the Goeritz method that generalizes the Goeritz matrix for computing the HOMFLY–PT polynomials for any <span>(N)</span> in the special case of bipartite links. Our method reduces to purely algebraic operations on matrices, and therefore, it can easily be implemented as a computer program. Bipartite links form a rather large family, including a special class of Montesinos links constructed from the so-called rational tangles. We demonstrate how to obtain a bipartite diagram of such links and calculate the corresponding HOMFLY–PT polynomials using our developed generalized Goeritz method. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 1","pages":"21 - 65"},"PeriodicalIF":1.1,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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