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Exact solutions and Bäcklund transformations for an extended second Painlevé equation 一类扩展二阶painlevleve方程的精确解和Bäcklund变换
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090090
A. Pickering, Á. Torres Sánchez
{"title":"Exact solutions and Bäcklund transformations for an extended second Painlevé equation","authors":"A. Pickering,&nbsp;Á. Torres Sánchez","doi":"10.1134/S0040577925090090","DOIUrl":"10.1134/S0040577925090090","url":null,"abstract":"<p> We consider an extended version of the second Painlevé equation <span>((mathrm P_{mathrm{II}}))</span>, which appears as the simplest member of a recently-derived extended second Painlevé hierarchy. For this third-order system we consider the application of the Ablowitz–Ramani–Segur algorithm, use its auto-Bäcklund transformations ( auto-BTs) to construct sequences of rational solutions and solutions defined in terms of Bessel functions, the latter constituting the analogues for the extended <span>(mathrm P_{mathrm{II}})</span> of the well-known Airy function solutions of <span>(mathrm P_{mathrm{II}})</span>. In addition, we present two new Bäcklund transformations, which extend the Schwarzian <span>(mathrm P_{mathrm{II}})</span> equation due to Weiss and an auto-BT due to Gambier. Finally, we use the auto-BTs of extended <span>(mathrm P_{mathrm{II}})</span> also to derive a new third-order discrete system. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1653 - 1663"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169644","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
Implicit quiescent solitons in optical metamaterials with an array of self-phase modulation structures by Lie symmetry 具有李氏对称自相位调制结构阵列的光学超材料中的隐式静态孤子
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI: 10.1134/S0040577925090016
A. R. Adem, A. Biswas, Y. Yildirim
{"title":"Implicit quiescent solitons in optical metamaterials with an array of self-phase modulation structures by Lie symmetry","authors":"A. R. Adem,&nbsp;A. Biswas,&nbsp;Y. Yildirim","doi":"10.1134/S0040577925090016","DOIUrl":"10.1134/S0040577925090016","url":null,"abstract":"<p> We find implicit quiescent solitons in optical metamaterials with nonlinear chromatic dispersion and several forms of self-phase modulation structures. The temporal evolution is however assumed to be linear. Some of the self-phase modulation structures yield results with quadratures. In each case, the governing model is integrated by applying Lie symmetry. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 3","pages":"1509 - 1526"},"PeriodicalIF":1.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170026","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 a weak periodic internal layer in a problem with a discontinuous reaction 不连续反应问题中的弱周期内层
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080069
E. I. Nikulin, A. V. Karamyshev
{"title":"On a weak periodic internal layer in a problem with a discontinuous reaction","authors":"E. I. Nikulin,&nbsp;A. V. Karamyshev","doi":"10.1134/S0040577925080069","DOIUrl":"10.1134/S0040577925080069","url":null,"abstract":"<p> We consider a boundary value problem with a time-periodic condition for an equation of “reaction–advection–diffusion” type with weak smooth advection and with reaction discontinuous in the spatial coordinate. We construct the asymptotics, prove the existence, and investigate the stability of periodic solutions with the constructed asymptotics and with a weak internal layer formed near the discontinuity point. To construct the asymptotics, we use the Vasil’eva method; to justify the existence of the solution, the asymptotic method of differential inequalities; and to study stability, the method of contracting barriers. We show that such a solution, as a solution of the corresponding initial-boundary value problem, is asymptotically Lyapunov stable. We determine the stability domain of a finite (not asymptotically small) width for such a solution and prove that the solution of the periodic problem is unique in this domain. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1414 - 1427"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891356","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 energy–momentum tensor of the causally disconnected region of the universe, the cosmological constant, and the multiverse 宇宙中因果分离区域的能量-动量张量，宇宙常数和多元宇宙
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080124
V. I. Kochkin
{"title":"The energy–momentum tensor of the causally disconnected region of the universe, the cosmological constant, and the multiverse","authors":"V. I. Kochkin","doi":"10.1134/S0040577925080124","DOIUrl":"10.1134/S0040577925080124","url":null,"abstract":"<p> We continue studying the phenomenological model in which dark energy in the form of the cosmological constant is identified with the mean of the energy–momentum tensor of the causally disconnected region. We show that the proposed model leads to multiple birth of universes. The study of the potential of the scalar field corresponding to this approach allows finding a connection between fluctuations in the energy of the true vacuum in the background space and the beginning of the inflationary stage. The previous universe acts as a background space at the moment of separation of the new universe. As a result, we obtain another explanation for the small value of the true cosmological constant. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1497 - 1508"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891358","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
Cycles with the embedded bursting effect in a circle of neural oscillators 在一圈神经振荡器中嵌入爆破效应的周期
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080094
I. D. Voronov, M. M. Preobrazhenskaia, I. V. Teplyashin
{"title":"Cycles with the embedded bursting effect in a circle of neural oscillators","authors":"I. D. Voronov,&nbsp;M. M. Preobrazhenskaia,&nbsp;I. V. Teplyashin","doi":"10.1134/S0040577925080094","DOIUrl":"10.1134/S0040577925080094","url":null,"abstract":"<p> We consider a model of a circular network of neurons where the functioning of each neuron is described by an equation with two delays. The model under study is a modification considered in the paper of Glyzin et al., where the model of a solitary neuron is based on of the equation with one delay—the Hutchinson equation. We construct discrete traveling waves, i.e., a periodic solution of the system such that all components coincide with the same function shifted by a quantity that is multiple of a certain parameter. To find this solution, we study an auxiliary differential-difference equation of the Volterra type with three delays. For this equation, for any natural <span>(m)</span> and <span>(n)</span>, we establish the existence of a periodic solution that contains <span>(m)</span> packets, each of which contains <span>(n)</span> bursts per period. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1452 - 1469"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891537","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
Noncommutative (n)-torus in the magnetic field: volume, scalar curvature, and quantum stochastic equation 不可交换(n) -磁场中的环面：体积，标量曲率和量子随机方程
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080033
M. N. Hounkonnou, F. Melong
{"title":"Noncommutative (n)-torus in the magnetic field: volume, scalar curvature, and quantum stochastic equation","authors":"M. N. Hounkonnou,&nbsp;F. Melong","doi":"10.1134/S0040577925080033","DOIUrl":"10.1134/S0040577925080033","url":null,"abstract":"<p> Motivated by the works published in 2003 by Chakraborty <i>et al.</i> [<i>J. Operator Theory</i>, <b>49</b> (2003), 185–201], and by Sakamoto and Tanimura [<i>J. Math. Phys.</i>, <b>44</b> (2003), 5042–5069], we investigate the noncommutative <span>(n)</span>-torus in a magnetic field. We study the invariance of volume, integrated scalar curvature, and volume form using the method of perturbation by the inner derivation of the magnetic Laplacian in this geometric framework. Moreover, we derive the magnetic stochastic process describing the motion of a particle in a uniform magnetic field in this torus and deduce the properties of solutions of the corresponding magnetic quantum stochastic differential equation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1340 - 1358"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891541","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
Cellular quantum billiards generating Boolean algebra representations 生成布尔代数表示的细胞量子台球
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080082
S. A. Titarenko
{"title":"Cellular quantum billiards generating Boolean algebra representations","authors":"S. A. Titarenko","doi":"10.1134/S0040577925080082","DOIUrl":"10.1134/S0040577925080082","url":null,"abstract":"<p> We introduce a new doubly unitary operator (isospectry) on wave functions, whose existence is equivalent to the equality of the spectra of two quantum billiards. It generates a map of nested billiards (induced reflection) with rich properties. This allows proving that in addition to isometry there is a unique realization of isospectrality of billiards, namely, a multivalued isometry. Then they are cellular and are constructed by reflections of the same cell. The algebra of their cellular subsets is isomorphic to a complete Boolean algebra and leads to the known generalized double negation formula, which corresponds to the logical foundations of quantum theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1437 - 1451"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891359","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
Shirokov canonical parameterization of local operators in modern problems of the hadron structure 强子结构现代问题中局部算子的Shirokov正则参数化
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080100
A. F. Krutov, V. E. Troitsky
{"title":"Shirokov canonical parameterization of local operators in modern problems of the hadron structure","authors":"A. F. Krutov,&nbsp;V. E. Troitsky","doi":"10.1134/S0040577925080100","DOIUrl":"10.1134/S0040577925080100","url":null,"abstract":"<p> We discuss the general method of parameterization of matrix elements of local operators developed by Yu. M. Shirokov. This method is a core of one of the successful variants of the relativistic composite model developed by the authors, namely, the instant form of Dirac relativistic dynamics, which gives good results when describing composite quark and nucleon systems. Using the Shirokov parameterization, we construct operators of the electromagnetic current and the energy–momentum tensor of a composite system taking the Lorentz covariance and the conservation into account. As an example, we derive formulas for the electric and gravitational form factors of a pion. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1470 - 1485"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891494","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 negative symmetry classification problem 负对称分类问题
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S0040577925080057
M. P. Kolesnikov
{"title":"The negative symmetry classification problem","authors":"M. P. Kolesnikov","doi":"10.1134/S0040577925080057","DOIUrl":"10.1134/S0040577925080057","url":null,"abstract":"<p> We introduce a method for constructing negative symmetries from consistent triples of differential and differential-difference equations. We also study the relation between <span>(3)</span>D consistent equations in the discrete and continuous case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1398 - 1413"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891543","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 the solution of a system of singularly perturbed differential equations in the forest fire spread models 森林火灾蔓延模型中一类奇摄动微分方程系统解的渐近性
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI: 10.1134/S004057792508001X
R. L. Argun, N. T. Levashova, E. V. Polezhaeva
{"title":"Asymptotics of the solution of a system of singularly perturbed differential equations in the forest fire spread models","authors":"R. L. Argun,&nbsp;N. T. Levashova,&nbsp;E. V. Polezhaeva","doi":"10.1134/S004057792508001X","DOIUrl":"10.1134/S004057792508001X","url":null,"abstract":"<p> We propose a forest fire model consisting of two equations, namely those describing the motion of the temperature front and the burned biomass front. To obtain a physically meaningful description of the solution behavior, we use equations with modular nonlinearity. For the proposed models, using asymptotic analysis methods, we have studied the existence of a solution in the form of a front. The asymptotic analysis allows us to estimate the speed of the front and determine the limits of the model applicability. When generalized to the two-dimensional case, the model can be used to simulate the motion of the combustion front in real forest fires, as well as to pose inverse problems for determining the amount of burned biomass after the passage of the combustion front. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 2","pages":"1311 - 1323"},"PeriodicalIF":1.1,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891539","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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