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Three-loop gauge beta functions in supersymmetric theories with exponential higher covariant derivative regularization 指数高协变导数正则化超对称理论中的三环规范函数
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100119
S. K. Singh
{"title":"Three-loop gauge beta functions in supersymmetric theories with exponential higher covariant derivative regularization","authors":"S. K. Singh","doi":"10.1134/S0040577926100119","DOIUrl":"10.1134/S0040577926100119","url":null,"abstract":"<p> We study the three-loop gauge <span>(beta)</span>-functions in general <span>(mathcal N=1)</span> supersymmetric gauge theories regularized by higher-covariant-derivatives (HCD) supplemented with Pauli–Villars subtraction. The all-structure three-loop form of the <span>(beta)</span>-functions in the HCD framework is known and involves regulator-dependent parameters. Here we evaluate these parameters explicitly for the exponential regulators <span>(R(x)=e^{x^n})</span> and <span>(F(x)=e^{x^m})</span>. We obtain the constants <span>(A(n))</span> and <span>(B(m))</span> in closed form, together with their large-<span>(n,m)</span> asymptotics, and substitute them into the general three-loop expressions. This yields fully explicit, regulator-parameterized <span>(beta)</span>-functions and a systematic expansion in <span>(1/n)</span> and <span>(1/m)</span> that organizes finite, scheme-dependent terms. We then introduce finite coupling redefinitions that map the renormalized <span>(overline{mathrm{DR}})</span> result to a scheme compatible with the Novikov–Shifman–Vainshtein–Zakharov relation. Our analysis clarifies how exponential higher-derivative regulators preserve this relation at the bare level and illustrates the regulator-driven structure of supersymmetric renormalization group flows. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1853 - 1873"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230615","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
Planetary link of the trefoil knot 三叶结的行星连杆
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100016
D. A. Baranov, E. V. Nozdrinova, O. V. Pochinka
{"title":"Planetary link of the trefoil knot","authors":"D. A. Baranov,&nbsp;E. V. Nozdrinova,&nbsp;O. V. Pochinka","doi":"10.1134/S0040577926100016","DOIUrl":"10.1134/S0040577926100016","url":null,"abstract":"<p> In this paper, we provide a partial solution to the Birman–Williams problem on describing the planetary link of a fibered knot <span>(Ksubsetmathbb S^3)</span>. Using Nielsen’s classification theory of periodic homeomorphisms of surfaces and its close connection with the theory of gradient-like diffeomorphisms, we prove that the planetary link of the trefoil knot (the unique periodic fibered knot of genus <span>(1)</span>) is the link consisting of the trefoil and the Hopf link. Furthermore, we classify all flows on the 3-sphere <span>(mathbb{S}^3)</span> that realize the planetary link of the trefoil, i.e., structurally stable flows with a minimal number of periodic orbits transverse to the fibration of the trefoil. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1701 - 1710"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230606","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
To the problem of the instability of the charged liquid surface bearing a surfactant film 针对表面活性剂膜带电液体表面的不稳定性问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100028
D. F. Belonozhko
{"title":"To the problem of the instability of the charged liquid surface bearing a surfactant film","authors":"D. F. Belonozhko","doi":"10.1134/S0040577926100028","DOIUrl":"10.1134/S0040577926100028","url":null,"abstract":"<p> We reveal the most general regularities of the surface distribution of compressions and stretches in a surfactant film distributed on a liquid surface, which is in an unstable state with respect to the excess of the surface electric charge. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1711 - 1716"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230585","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
Hyperbolic equations with higher symmetries of the fifth order 具有五阶高对称性的双曲方程
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S004057792610003X
R. N. Garifullin
{"title":"Hyperbolic equations with higher symmetries of the fifth order","authors":"R. N. Garifullin","doi":"10.1134/S004057792610003X","DOIUrl":"10.1134/S004057792610003X","url":null,"abstract":"<p> We classify hyperbolic-type equations and study the class of equations in the form </p><p> where <span>(u(x,y))</span> is the unknown function and <span>(x,y)</span> are independent variables. The classification is based on the requirement for the existence of higher symmetries of the fifth order. As a result, we obtain a list of four equations satisfying the specified conditions. One of these equations is new. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1717 - 1724"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230607","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
Stationary solution in a Tikhonov-type system in the case of discontinuity of advection coefficients and nonlinear source terms 平流系数不连续和非线性源项情况下tikhonov型系统的平稳解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100065
E. A. Chunzhuk, N. T. Levashova, E. I. Nikulin
{"title":"Stationary solution in a Tikhonov-type system in the case of discontinuity of advection coefficients and nonlinear source terms","authors":"E. A. Chunzhuk,&nbsp;N. T. Levashova,&nbsp;E. I. Nikulin","doi":"10.1134/S0040577926100065","DOIUrl":"10.1134/S0040577926100065","url":null,"abstract":"<p> The present work is devoted to a system of fast and slow equations with spatially discontinuous nonlinear advection coefficients and source functions. We investigate a solution with an internal transition layer localized near the discontinuity point. This study continues earlier research on stationary fast-slow systems of the reaction–diffusion–advection type, in which a boundary-layer solution of a similar problem with smooth advection coefficients and reactive terms was considered. Furthermore, this work is a natural extension of an earlier investigation of a similar system with discontinuous reactive terms but without advective terms, and addresses the question of the influence of these advective terms on the structure of the transition layer. The main results include the construction of an asymptotic approximation for the stationary solution, alongside proofs of its existence and asymptotic stability as a solution of the corresponding initial-boundary value problem. The proof is based on the asymptotic method of differential inequalities. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1774 - 1793"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230608","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 solution of the Wiener–Hopf equation of the first kind with a symmetric kernel 带对称核的第一类Wiener-Hopf方程的解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100132
N. B. Yengibaryan
{"title":"On the solution of the Wiener–Hopf equation of the first kind with a symmetric kernel","authors":"N. B. Yengibaryan","doi":"10.1134/S0040577926100132","DOIUrl":"10.1134/S0040577926100132","url":null,"abstract":"<p> The equation <span>(displaystyleint_{0}^{infty} T(|x - t|)f(t),dt = g(x))</span>, where the functions <span>(T)</span> and <span>(g)</span> satisfy certain smoothness, monotonicity, and integrability conditions, is considered. By applying double differentiation, an exact solution to this equation is constructed in terms of locally integrable functions and the Dirac delta function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1890 - 1895"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230617","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
Integrability and exact solutions of the nonuniform Hirota equation with variable coefficients 变系数非均匀Hirota方程的可积性与精确解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100090
Jiangying Huo, Taogetusang Bao
{"title":"Integrability and exact solutions of the nonuniform Hirota equation with variable coefficients","authors":"Jiangying Huo,&nbsp;Taogetusang Bao","doi":"10.1134/S0040577926100090","DOIUrl":"10.1134/S0040577926100090","url":null,"abstract":"<p> We study the integrability problem of the nonuniform Hirota (vc-Hirota) equation with variable coefficients by using the Bell polynomial method and the Darboux transformation (DT). The nonuniform vc-Hirota equation describes the wave propagation of picosecond pulses more accurately than the nonlinear Schrödinger (NLS) equation. Firstly, by using the Bell polynomial method, we construct the Bäcklund transformation (BT) and Lax pair of the equation to prove that the nonuniform vc-Hirota equation is Lax integrable. Interestingly, the Lax pair we constructed has variable coefficients and is nonisospectral, as opposed to having constant coefficients. Secondly, by pairing the Lax pair with the zero-curvature equation, we obtain the DT of the equation. Finally, we construct the soliton-like solutions of the equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1811 - 1832"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230609","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 the modified Korteweg–de Vries equation of negative order in the case of multiple eigenvalues 修正Korteweg-de Vries方程在多重特征值情况下的负阶积分
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100077
G. U. Urazboev, I. I. Baltaeva
{"title":"Integration of the modified Korteweg–de Vries equation of negative order in the case of multiple eigenvalues","authors":"G. U. Urazboev,&nbsp;I. I. Baltaeva","doi":"10.1134/S0040577926100077","DOIUrl":"10.1134/S0040577926100077","url":null,"abstract":"<p> The modified Korteweg–de Vries equation of negative order is investigated by the inverse scattering transform method in the case where the corresponding non-self-adjoint Dirac-type operator has a finite number of discrete multiple eigenvalues of a given multiplicity. The evolution laws of the scattering data, including the normalization chains corresponding to the multiple eigenvalues, are derived. A representation of the solution to the Cauchy problem is constructed based on the Gelfand–Levitan–Marchenko integral equations adapted to the degenerate spectral structure. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1794 - 1802"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230610","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
Rotated-spheroid Earth model: Symmetry, mass redistribution, and the role of high-discharge rivers 旋转球体地球模型：对称性、质量再分配和高流量河流的作用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100144
V. N. Nikolić
{"title":"Rotated-spheroid Earth model: Symmetry, mass redistribution, and the role of high-discharge rivers","authors":"V. N. Nikolić","doi":"10.1134/S0040577926100144","DOIUrl":"10.1134/S0040577926100144","url":null,"abstract":"<p> In this study, a symmetry analysis is performed in order to probe the impact of rivers on the Earth’s mass balance within a new symmetry framework. As a river of the highest discharge, the Amazon River was modeled to probe its impact on continental mass redistribution. It was shown that roughly 1% of South America’s continental mass would be separated from the Upper Amazon Basin within 155 years, progressing sequentially along the river to reach 10% near the Amazon mouth over 1550 years. The resulting asymmetry in mass distribution is illustrated by synthetic two-dimensional hysteresis curves, confirming the river’s role as a localized symmetry-breaking factor. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1896 - 1905"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230614","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
Fast traveling wave in a hyperbolic equation 双曲方程中的快速行波
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-10-22 DOI: 10.1134/S0040577926100120
L. A. Kalyakin
{"title":"Fast traveling wave in a hyperbolic equation","authors":"L. A. Kalyakin","doi":"10.1134/S0040577926100120","DOIUrl":"10.1134/S0040577926100120","url":null,"abstract":"<p> We investigate a supercritical traveling wave as a solution to a hyperbolic semilinear partial differential equation and establish the conditions for its existence. We focus primarily on the stability problem, which leads us to analyze a spectral problem for a non-self-adjoint operator. Finally, we describe a wide class of initial perturbations with respect to which the wave exhibits asymptotic stability in the linear approximation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"229 1","pages":"1874 - 1889"},"PeriodicalIF":1.0,"publicationDate":"2026-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149230584","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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