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Existence and stability of stationary two-dimensional solutions with boundary layers arising in the drift-diffusion model of semiconductors with subDebye dimensions 具有亚德拜维的半导体漂移扩散模型中具有边界层的二维平稳解的存在性和稳定性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090072
E. I. Nikulin, A. V. Karamyshev
{"title":"Existence and stability of stationary two-dimensional solutions with boundary layers arising in the drift-diffusion model of semiconductors with subDebye dimensions","authors":"E. I. Nikulin,&nbsp;A. V. Karamyshev","doi":"10.1134/S0040577926090072","DOIUrl":"10.1134/S0040577926090072","url":null,"abstract":"<p> We study stationary solutions with boundary layers of singularly perturbed Tikhonov-type systems of reaction–advection–diffusion equations arising in the drift-diffusion model of semiconductors with subDebye dimensions in the two-dimensional case. We construct a boundary-layer asymptotics of solutions in the case of Dirichlet boundary conditions. To prove theorems on the existence and the asymptotic Lyapunov stability of such solutions, we use the asymptotic method of differential inequalities. The obtained results can be applied to the drift-diffusion model of semiconductors with the subDebye dimensions: we find the distribution of electrons and holes in a ring-shaped sample. We construct the asymptotics of the total recombination density function and find its extrema as functions of temperatures. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1581 - 1599"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011461","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 existence, uniqueness, and stability of the limit cycle of the Mackey–Glass equation 关于Mackey-Glass方程极限环的存在唯一性和稳定性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090011
V. V. Alekseev
{"title":"On the existence, uniqueness, and stability of the limit cycle of the Mackey–Glass equation","authors":"V. V. Alekseev","doi":"10.1134/S0040577926090011","DOIUrl":"10.1134/S0040577926090011","url":null,"abstract":"<p> We investigate oscillations in the Mackey–Glass equation under the assumption that the exponent in the denominator of the nonlinear term is a large parameter. We consider the case in which the limiting relay equation obtained as the large parameter tends to infinity has a periodic solution with the minimum number of switchings per period. For this case, we prove the existence and uniqueness of an exponentially orbitally stable limit cycle of the Mackey–Glass equation that is asymptotically close to the periodic solution of the limiting equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1487 - 1493"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011469","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
Front motion in a problem with nonlinear diffusion 非线性扩散问题中的锋面运动
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090060
A. R. Makhmudov, A. O. Orlov, E. I. Nikulin, R. L. Argun
{"title":"Front motion in a problem with nonlinear diffusion","authors":"A. R. Makhmudov,&nbsp;A. O. Orlov,&nbsp;E. I. Nikulin,&nbsp;R. L. Argun","doi":"10.1134/S0040577926090060","DOIUrl":"10.1134/S0040577926090060","url":null,"abstract":"<p> We consider a singularly perturbed initial-boundary value problem for a parabolic equation with nonlinear diffusion. A moving-front type solution is studied. Using the Vasil’eva method of boundary functions, we construct a formal asymptotic approximation to the solution with respect to a small parameter. A differential equation defining the law of motion of the front is derived. Based on Nefedov’s method of differential inequalities, a theorem on the existence and uniqueness of the solution is proved. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1565 - 1580"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011471","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
Wave dynamics of osculating pseudo null flow from anholonomic perspective 从非完整角度看模拟伪零流的波动动力学
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080088
M. Erdoğdu, A. Yavuz
{"title":"Wave dynamics of osculating pseudo null flow from anholonomic perspective","authors":"M. Erdoğdu,&nbsp;A. Yavuz","doi":"10.1134/S0040577926080088","DOIUrl":"10.1134/S0040577926080088","url":null,"abstract":"<p> In this study, the evolution of electromagnetic wave vectors along pseudo-null curves defined in Minkowski space has been investigated using anholonomic coordinates. By considering the tangential and normal osculating flows of the curves, the effects of changes in the geometric structure on the propagation and direction of electromagnetic waves have been investigated. By establishing relationships between the electric and magnetic field vectors using the pseudo-null frame, wave equations dependent on Bishop curvature functions have been derived. Furthermore, it has been shown that the surfaces produced by the osculating flows belong to degenerate geometric structures. The findings provide a new geometric perspective on the relationship between differential geometry and electromagnetic wave theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1388 - 1397"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807357","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
Integration of a mixed problem on the half-axis for the system of Kaup equations Kaup方程组半轴上混合问题的积分
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080027
A. B. Yakhshimuratov, O. M. Matyokubov
{"title":"Integration of a mixed problem on the half-axis for the system of Kaup equations","authors":"A. B. Yakhshimuratov,&nbsp;O. M. Matyokubov","doi":"10.1134/S0040577926080027","DOIUrl":"10.1134/S0040577926080027","url":null,"abstract":"<p> A system of nonlinear Kaup equations on the half-axis is considered in the class of functions rapidly decreasing with respect to the spatial variable. An equation is derived for describing the evolution of the Weyl function of a quadratic pencil of Sturm–Liouville equations on the half-axis, whose coefficients are the solution of a mixed problem posed for the system of nonlinear Kaup equations. The obtained results allow the integration of the system of nonlinear Kaup equations on the half-axis using the inverse scattering method. An algorithm for solving the mixed problem for the nonlinear Kaup system in the class of functions rapidly decreasing with respect to the spatial variable is obtained. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1294 - 1303"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807353","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
Orlov–Schulman symmetries of the self-dual conformal structure equations 自对偶共形结构方程的Orlov-Schulman对称性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080015
L. V. Bogdanov
{"title":"Orlov–Schulman symmetries of the self-dual conformal structure equations","authors":"L. V. Bogdanov","doi":"10.1134/S0040577926080015","DOIUrl":"10.1134/S0040577926080015","url":null,"abstract":"<p> We construct Orlov–Schulman symmetries for the self-dual conformal structure (SDCS) hierarchy. An explicit proof of the compatibility of additional symmetries with the basic Lax–Sato flows of the hierarchy is provided, and several simple examples, including Galilean transformations and scalings, are considered. We also present a picture of the Orlov–Schulman symmetries in terms of a dressing scheme based on the Riemann–Hilbert problem. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1283 - 1293"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807358","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 TAMSD distributions for turbulent plasma density time series 湍流等离子体密度时间序列TAMSD分布的渐近性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S004057792608012X
N. S. Arkashov
{"title":"Asymptotics of TAMSD distributions for turbulent plasma density time series","authors":"N. S. Arkashov","doi":"10.1134/S004057792608012X","DOIUrl":"10.1134/S004057792608012X","url":null,"abstract":"<p> The paper analyzes a stationary plasma density time series recorded in the peripheral confinement region of a thermonuclear device. This series exhibits the long-range dependence effect. To construct independent analogs of the time series, the inverse distribution function method for modeling stationary non-Gaussian processes is employed. This modeling of experimental reproducibility allows for the identification of physical patterns that govern the distributions of statistical characteristics derived from empirical data. Special attention is paid to the asymptotic convergence of the distributions of the centered and normalized time-averaged mean square displacement (TAMSD). From a physical perspective, the proposed approach provides a mathematical framework for the probabilistic assessment of extreme plasma density fluctuations, which, in real devices, can lead to peak heat loads on the first-wall components of the reactor. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1456 - 1472"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807351","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
Localized wave solutions of three-component defocusing Kundu–Eckhaus equation with (4times4) matrix spectral problem 具有(4times4)矩阵谱问题的三分量离焦Kundu-Eckhaus方程的局域波解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080040
Yanan Wang, Min Xue
{"title":"Localized wave solutions of three-component defocusing Kundu–Eckhaus equation with (4times4) matrix spectral problem","authors":"Yanan Wang,&nbsp;Min Xue","doi":"10.1134/S0040577926080040","DOIUrl":"10.1134/S0040577926080040","url":null,"abstract":"<p> This work focuses on the three-component defocusing Kundu–Eckhaus equation, which serves as a significant coupled model for describing complex wave propagation in nonlinear optical fibers. By employing the binary Darboux transformation based on a <span>(4times4)</span> matrix spectral problem, we derive vector dark soliton solutions, while the exact expressions of asymptotic dark soliton components are obtained through an asymptotic analysis method. Furthermore, breather and Y-shaped breather solutions, absent from single-component defocusing Kundu–Eckhaus systems, are obtained due to the mutual coupling effects between different components. The results significantly advance our understanding of nonlinear wave phenomena induced by coupling effects and provide a theoretical reference for subsequent studies on defocusing multi-component systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1315 - 1327"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807356","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 zero-range potential and vacuum polarization of a scalar field 标量场的二维零范围势和真空极化
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080106
P. A. Spirin
{"title":"Two-dimensional zero-range potential and vacuum polarization of a scalar field","authors":"P. A. Spirin","doi":"10.1134/S0040577926080106","DOIUrl":"10.1134/S0040577926080106","url":null,"abstract":"<p> We consider two problems related to the emergence and use of a two-dimensional delta-like potential: on a plane and in a three-dimensional space. We propose a nonperturbative calculation of the Green’s functions of a massless real scalar field <span>(phi)</span>. For an effectively two-dimensional zero-range potential, we compare two methods for calculating the Green’s functions: as a self-adjoint extension of the Laplacian on a plane with a punctured point and as a result of incomplete Fourier transforms with the direct action of the delta function. The second method involves the renormalization of the interaction coupling constant, as prescribed by the analogous quantum-mechanical problem. We present the regularized Green’s functions in three equivalent integral forms: as products of Bessel functions of the first kind, as products of modified Bessel functions, and as products of Kelvin functions. Using the Green’s function, we calculate the vacuum expectation value <span>(langle phi^2rangle)</span> as well as the renormalized energy-momentum tensor operator. The two approaches yield equivalent results, which confirms the prescriptions imposed during the derivation in particular cases. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1426 - 1448"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807352","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
Emission of pairs of neutrinos by a variable field in the second Born approximation. Effective Lagrangian of the photon–neutrino interaction 在第二个玻恩近似中，由可变场发射的中微子对。光子-中微子相互作用的有效拉格朗日量
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-08-25 DOI: 10.1134/S0040577926080118
V. V. Skobelev
{"title":"Emission of pairs of neutrinos by a variable field in the second Born approximation. Effective Lagrangian of the photon–neutrino interaction","authors":"V. V. Skobelev","doi":"10.1134/S0040577926080118","DOIUrl":"10.1134/S0040577926080118","url":null,"abstract":"<p> We consider the generation of a pair of neutrinos by a variable classical electromagnetic field in the second Born approximation, which is analogous to the nonlinear effect of photon emission under the same conditions. This effect is of interest for extending the nonlinear processes of quantum electrodynamics to other particles with zero or vanishingly small masses, such as neutrinos. We find a class of fields for which this effect does not exist, in contrast to the quantum electrodynamics effects discussed in previous papers written with the participation of the author. The effective Lagrangian of the photon–neutrino interaction is obtained for the first time. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 2","pages":"1449 - 1455"},"PeriodicalIF":1.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148807361","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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