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Accelerating barotropic fluid cosmological model in (f(R,T)) gravity (f(R,T))重力中的加速正压流体宇宙学模型
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030104
S. K. Sahu, M. Ota, B. K. Bishi
{"title":"Accelerating barotropic fluid cosmological model in (f(R,T)) gravity","authors":"S. K. Sahu,&nbsp;M. Ota,&nbsp;B. K. Bishi","doi":"10.1134/S0040577926030104","DOIUrl":"10.1134/S0040577926030104","url":null,"abstract":"<p> A novel analytical approach is used to achieve an exact solution of the Bianchi type- III spacetime in the context of <span>(f(R,T))</span> gravity. Two functional forms are considered: <span>(f(R,T)=R+2f_1(T)=R+2mu T)</span> and <span>(f(R,T)=f_1(R)+f_2(T)=R+alpha R^2+mu T)</span>. The solution is achieved assuming a barotropic fluid, which actually produces a vacuum energy. In mathematical terms, it is equivalent to the cosmological constant <span>(Lambda)</span>. The resulting spacetime is found to be anisotropic and homogeneous. In addition, the stability of the model is examined, and numerous physical properties are discussed in detail for the case of <span>(f(R,T)=R+2mu T)</span>. In contrast, the nonlinear case, <span>(f(R,T)=R+alpha R^2+mu T)</span>, reduces to a self-consistent vacuum solution characterized by <span>(A_1=pm t)</span>, <span>(A_2=t)</span>, and <span>(A_3=1)</span>. In this configuration, the modified field equations reduce to those of general relativity in vacuum, demonstrating that the higher-order curvature term <span>(alpha R^2)</span> and the matter coupling term <span>(mu T)</span> do not influence the cosmic dynamics. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"546 - 558"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561363","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
Dynamics of three-dimensional localized wave packets defined by the spherical Bessel function (mathbf{j}_0(x)) 球面贝塞尔函数定义的三维局域波包动力学 (mathbf{j}_0(x))
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030086
S. Yu. Dobrokhotov, A. V. Tsvetkova
{"title":"Dynamics of three-dimensional localized wave packets defined by the spherical Bessel function (mathbf{j}_0(x))","authors":"S. Yu. Dobrokhotov,&nbsp;A. V. Tsvetkova","doi":"10.1134/S0040577926030086","DOIUrl":"10.1134/S0040577926030086","url":null,"abstract":"<p> We consider a localized wave packet which is an asymptotic solution to the three-dimensional wave equation and is generated by the spherical Bessel function <span>(mathbf{j}_0)</span> at the initial time. We discuss an approach for constructing an effective representation for such a packet in terms of special functions, based on the theory of the Maslov canonical operator and the study of the dynamics of the corresponding three-dimensional Lagrangian manifold. In particular, we prove that if the initial packet has a large momentum directed along the <span>(x_3)</span> axis, then the Bessel structure eventually vanishes and the packet spreads. Specifically, on the corresponding Lagrangian manifold, there arise singularities of the fold and cusp types, which are associated with the Airy and Pearcey functions, respectively, as well as non-generic singularities corresponding to the asymptotics in terms of the error function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"499 - 522"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561364","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
Regular line-solitons of modified KP system and vertex operators 修正KP系统的正则线孤子与顶点算子
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030049
Conghui Li, Chuanzhong Li
{"title":"Regular line-solitons of modified KP system and vertex operators","authors":"Conghui Li,&nbsp;Chuanzhong Li","doi":"10.1134/S0040577926030049","DOIUrl":"10.1134/S0040577926030049","url":null,"abstract":"<p> In this paper, we study the effects of vertex operators on soliton solutions of the modified Kadomtsev–Petviashvili (mKP) equation based on the Grassmannian <span>(Gr(N, M))</span>. We present a classification theorem for the solutions of the mKP equation and demonstrate the connection among vertex operators, theta functions, and the tau-function of the mKP equation. We also express the soliton solution on <span>(Gr(N,M))</span> of the mKP equation in terms of the <span>(M)</span>-theta function and free fermions. We show that the new tau-function obtained by the action of the vertex operator on the tau-function of the mKP equation can still form a solution of the mKP equation. We study all kinds of solutions of the mKP equation obtained through the action of vertex operators. We find that when the mKP equation solutions obtained via the action of the vertex operator satisfy the regularity condition, the chord diagram exhibits non-crossing between the graph related to the parameters of the vertex operators and the graph related to the parameters of the original solution. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"423 - 447"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561830","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
Asymptotics of solutions of the Schrödinger equation with a two-dimensional quadratic inverted potential and localized right-hand side 具有二维二次逆势和右边定域的Schrödinger方程解的渐近性
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030050
O. O. Fedorov
{"title":"Asymptotics of solutions of the Schrödinger equation with a two-dimensional quadratic inverted potential and localized right-hand side","authors":"O. O. Fedorov","doi":"10.1134/S0040577926030050","DOIUrl":"10.1134/S0040577926030050","url":null,"abstract":"<p> We consider the Schrödinger equation with potential <span>(-x_1^2-bx_2^2)</span> and with a localized right-hand side. In this problem, the condition that the rays of the Hamiltonian system leave any finite region of the configuration space in finite time is not satisfied. Because of this, it is not possible to use the well-known algorithm for constructing an asymptotic solution in the form of a canonical operator on a certain Lagrangian manifold. We construct a solution to the equation in the form of an integral, express its asymptotics via known functions, and study the dependence of this solution on the parameter <span>(b)</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"448 - 469"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561360","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
Differential equations on manifolds and Lie algebras 流形与李代数上的微分方程
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030013
V. V. Zharinov
{"title":"Differential equations on manifolds and Lie algebras","authors":"V. V. Zharinov","doi":"10.1134/S0040577926030013","DOIUrl":"10.1134/S0040577926030013","url":null,"abstract":"<p> In this paper, we are starting to develop an algebraic approach to differential equations on smooth manifolds. As a first step, we present a general scheme of this approach, in which the planar case essentially coincides with the traditional formalism of partial differential equations. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"373 - 392"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561362","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
Jacobi inversion and solutions of Hitchin systems Hitchin系统的Jacobi反演与解
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030025
O. K. Sheinman
{"title":"Jacobi inversion and solutions of Hitchin systems","authors":"O. K. Sheinman","doi":"10.1134/S0040577926030025","DOIUrl":"10.1134/S0040577926030025","url":null,"abstract":"<p> We consider the separation of variables method for Hitchin systems with simple structure groups. We give a description of the invariant tori in terms of divisors on the spectral curve. We reduce the problem of finding a point on the trajectory of the system to solving algebraic equations. We formulate a criterion for the trajectories to be real. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"393 - 403"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561359","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
Spectral property for the 2D Zakharov–Kuznetsov equation 二维Zakharov-Kuznetsov方程的谱性质
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1134/S0040577926030037
S. Roudenko, J. Holmer
{"title":"Spectral property for the 2D Zakharov–Kuznetsov equation","authors":"S. Roudenko,&nbsp;J. Holmer","doi":"10.1134/S0040577926030037","DOIUrl":"10.1134/S0040577926030037","url":null,"abstract":"<p> We discuss a spectral property for the virial operator of the <span>(2)</span>D Zakharov–Kuznetsov (ZK) equation. This is a crucial ingredient to establish blow-up or asymptotic stability of solitary waves in higher-dimensional problems. This model in <span>(3)</span>D setting was originally introduced by Zakharov and Kuznetsov in plasma physics, and is also a higher-dimensional generalization of the well-known Korteweg–de Vries (KdV) equation. The problem of stability of solitary waves in ZK equation or stable blow-up in modified ZK (or KdV-type) equation is an important physical question, for which virial operators and their spectral properties are the essential elements of the analysis. In this paper we investigate this problem analytically and reduce it to verifying numerically only some signs of inner products and certain eigenvalues. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 3","pages":"404 - 422"},"PeriodicalIF":1.1,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561365","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 construction of integrable symplectic mappings 关于可积辛映射的构造
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020042
Xiao Yang, Mingyue Yu, Dianlou Du
{"title":"On the construction of integrable symplectic mappings","authors":"Xiao Yang,&nbsp;Mingyue Yu,&nbsp;Dianlou Du","doi":"10.1134/S0040577926020042","DOIUrl":"10.1134/S0040577926020042","url":null,"abstract":"<p> A stationary AKNS hierarchy is investigated through a new method for constructing integrable symplectic mappings. To achieve this, semi-discrete equations are derived from the AKNS spectral problem. Based on these equations, auto-transformations of the stationary AKNS equations are established. These auto-transformations are then used to generate integrable symplectic mappings. Additionally, group properties of these mappings are analyzed and presented. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"236 - 256"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341960","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
Different types of analytical solutions of the fifth-order KdV equation under the influence of Gaussian white noise and Brownian motion 高斯白噪声和布朗运动影响下的五阶KdV方程的不同类型解析解
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S0040577926020054
Hai-Yan Wang, Ying Shi, Song-Lin Zhao, Lu Yan
{"title":"Different types of analytical solutions of the fifth-order KdV equation under the influence of Gaussian white noise and Brownian motion","authors":"Hai-Yan Wang,&nbsp;Ying Shi,&nbsp;Song-Lin Zhao,&nbsp;Lu Yan","doi":"10.1134/S0040577926020054","DOIUrl":"10.1134/S0040577926020054","url":null,"abstract":"<p> In this paper, we consider the stochastic fifth-order KdV equation, along with its Lax pair, under the influence of Gaussian white noise and Brownian motion. One new result in this paper is that the soliton-periodic mixed solution can be viewed as a novel tool for generating rogue waves when the soliton solution is in the dominant position. By applying the classical Darboux transformation, we obtain analytic solutions to this equation in determinant form. Through detailed analysis of spectral parameters, we construct soliton solutions, periodic solutions, and their mixed solutions for the stochastic fifth-order KdV equation, which incorporates noise terms. We also consider the generalized Darboux transformation and obtain rational solutions to the stochastic fifth-order KdV equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"257 - 283"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341954","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
Global solvability, stability and oscillation criteria for systems of two first-order pseudo-linear ordinary differential equations 两个一阶伪线性常微分方程系统的全局可解性、稳定性和振荡准则
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-02-25 DOI: 10.1134/S004057792602008X
G. A. Grigorian
{"title":"Global solvability, stability and oscillation criteria for systems of two first-order pseudo-linear ordinary differential equations","authors":"G. A. Grigorian","doi":"10.1134/S004057792602008X","DOIUrl":"10.1134/S004057792602008X","url":null,"abstract":"<p> The Riccati equation method and other methods are used to establish global solvability, stability, and oscillation criteria for a class of two–dimensional nonlinear systems of ordinary differential equations. The class under study is a generalization of wide classes of second-order nonlinear ordinary differential equations, studied by many authors. The applicability of some of these criteria is illustrated by examples. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"226 2","pages":"313 - 337"},"PeriodicalIF":1.1,"publicationDate":"2026-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341959","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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