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Russian Journal of Mathematical Physics最新文献

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The Aspe-Depassier Equation with a Nonlinear Source: Reduction, Painlevé test, First Integrals and General Solutions 具有非线性源的Aspe-Depassier方程：约简，painlevest检验，一阶积分和通解
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825040119
N.A. Kudryashov
{"title":"The Aspe-Depassier Equation with a Nonlinear Source: Reduction, Painlevé test, First Integrals and General Solutions","authors":"N.A. Kudryashov","doi":"10.1134/S1061920825040119","DOIUrl":"10.1134/S1061920825040119","url":null,"abstract":"<p> A nonlinear partial differential equation describing waves in a convecting fluid with a nonlinear source is considered. Since the Cauchy problem is not solvable by the inverse scattering transform a traveling wave variables is employed to reduce the partial differential equation to fourth-order ordinary differential equation. The Painlevé test is used to derive the parameter constraints of the equation for its integrability. The relationship between the Fuchs indices obtained from the Painlevé test and the form of the first integrals is discussed. Guided by this information the first integrals are constructed. Under four parameter constraints obtained during Painlevé test general solution with four arbitrary constants are found. All such general solutions are expressed in terms of the transcendents of the first Painlev e equation, which are non-classical functions not reducible to known elementary functions. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"768 - 778"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Local Dynamics of an Equation with Two Large Proportional Delays 一类具有两个大比例时滞方程的局部动力学
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825601466
I.S. Kashchenko
{"title":"On the Local Dynamics of an Equation with Two Large Proportional Delays","authors":"I.S. Kashchenko","doi":"10.1134/S1061920825601466","DOIUrl":"10.1134/S1061920825601466","url":null,"abstract":"<p> Investigations of the local dynamics of singularly perturbed equations with two delays are carried out for the casein which both the delays are asymptotically large and, at the same time, of the same order (proportional). Critical cases were identified, and it was shown that all of them have infinite dimension. To study the behavior of solutions in cases close to critical, special nonlinear equations (quasinormal forms) were constructed whose solutions provide asymptotic approximations of the solutions to the original problem. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"728 - 744"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Internal Transition Layer in Reaction-Diffusion System in Bounded Domains 有界域上反应扩散系统的内过渡层
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825601569
K.A. Kotsubinsky, N.T. Levashova, A.O. Orlov
{"title":"Internal Transition Layer in Reaction-Diffusion System in Bounded Domains","authors":"K.A. Kotsubinsky,&nbsp;N.T. Levashova,&nbsp;A.O. Orlov","doi":"10.1134/S1061920825601569","DOIUrl":"10.1134/S1061920825601569","url":null,"abstract":"<p> The paper considers a system of two reaction-diffusion equations with diffusion coefficients differing by several orders of magnitude and discontinuous reactive terms. The existence, local uniqueness and Lyapunov asymptotic stability of a solution with an internal transition layer are established. The analysis is carried out using asymptotic method of differential inequalities. The obtained conditions for the existence of a stable solution determine the limits of applicability of model problems based on such systems of equations, in particular, for studying chemical transformations in the pore spaces of geological formations. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"755 - 767"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Existence and Stability of Stationary Solutions with Boundary Layers in a Tikhonov-Type System Arising in the Drift-Diffusion Model of Semiconductors of Sub-Debye-Length 亚德拜长度半导体漂移扩散模型中tikhonov型系统边界层平稳解的存在性与稳定性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825601533
A.V. Karamyshev, E.I. Nikulin
{"title":"Existence and Stability of Stationary Solutions with Boundary Layers in a Tikhonov-Type System Arising in the Drift-Diffusion Model of Semiconductors of Sub-Debye-Length","authors":"A.V. Karamyshev,&nbsp;E.I. Nikulin","doi":"10.1134/S1061920825601533","DOIUrl":"10.1134/S1061920825601533","url":null,"abstract":"<p> This paper investigates stationary boundary-layer solutions of singularly perturbed systems of Tikhonov-type equations arising in drift-diffusion models of sub-Debye semiconductors. Boundary-layer asymptotics for solutions are constructed for Neumann and Dirichlet boundary conditions. The asymptotic method of differential inequalities is used to prove the existence and asymptotic stability theorems for these solutions. A physical interpretation of the results thus obtained is provided. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"713 - 727"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Development of Methods for Asymptotic Analysis of Moving Fronts for the Reaction-Diffusion-Advection Equations 反应-扩散-平流方程运动锋渐近分析方法的发展
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825601454
A.O. Orlov, V.T. Volkov
{"title":"Development of Methods for Asymptotic Analysis of Moving Fronts for the Reaction-Diffusion-Advection Equations","authors":"A.O. Orlov,&nbsp;V.T. Volkov","doi":"10.1134/S1061920825601454","DOIUrl":"10.1134/S1061920825601454","url":null,"abstract":"<p> The present paper provides a survey of the achievements of the research group led by Professor N. N. Nefedov in the field of asymptotic analysis of moving fronts for nonlinear singularly perturbed reaction–diffusion–advection equations. The primary research tool is the asymptotic method of differential inequalities, which allows one to carry out a rigorous justification of the proposed asymptotic approximations. The paper systematizes results for parabolic initial-boundary value problems and illustrates key approaches to their analysis. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"803 - 817"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Large-Time Asymptotics of the Solution to a Certain System of Equations 一类方程组解的大时渐近性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S106192082560117X
M.O. Korpusov, A.A. Panin
{"title":"On Large-Time Asymptotics of the Solution to a Certain System of Equations","authors":"M.O. Korpusov,&nbsp;A.A. Panin","doi":"10.1134/S106192082560117X","DOIUrl":"10.1134/S106192082560117X","url":null,"abstract":"<p> This paper examines the global time solvability of the Cauchy problem for a nonlinear system of elliptic and parabolic equations. A large-time asymptotic solution to this Cauchy problem is obtained. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"745 - 754"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Semilinear Elliptic Equations on Star Graph with Small Edges 小边星图上的半线性椭圆方程
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825600515
M.N. Konyrkulzhayeva, D.I. Borisov
{"title":"Semilinear Elliptic Equations on Star Graph with Small Edges","authors":"M.N. Konyrkulzhayeva,&nbsp;D.I. Borisov","doi":"10.1134/S1061920825600515","DOIUrl":"10.1134/S1061920825600515","url":null,"abstract":"<p> We consider a second order semilinear elliptic equation on a star graph with finitely many edges, some of which are supposed to have small lengths proportional to a small parameter <span>(varepsilon.)</span> At the common vertex, a general boundary condition is imposed, while at the boundary vertices, we impose the Dirichlet or Robin or Neumann condition. The nonlinearity in the equation depends only on the unknown function and variable and is supposed to satisfy a Lipschitz condition as well as a certain monotonicity condition. In addition, the nonlinearity on the small edges is multiplied by <span>(varepsilon^{-1}.)</span> The main results of the paper establish the unique solvability of the considered problem and describe the convergence and asymptotic expansions for the solution as <span>(varepsilon)</span> goes to zero. The limiting problem is considered on the graph without small edges and involves a certain limiting boundary condition at the common vertex. This limiting boundary condition depends in a nontrivial nonlinear way on the nonlinearities in the original equation on the small edges. The convergence is established uniformly in <span>(L_2)</span>-norm of the right-hand side in the equation. We also construct the asymptotic expansion for the solution of perturbed problem up to an arbitrary power of <span>(varepsilon,)</span> and estimate the remainders in the asymptotics uniformly in <span>(L_2)</span>-norm of the right-hand side in the equation. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"634 - 661"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Achieving a Travelling Wave in a Hyperbolic Equation 双曲方程中行波的实现
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825040065
L.A. Kalyakin
{"title":"Achieving a Travelling Wave in a Hyperbolic Equation","authors":"L.A. Kalyakin","doi":"10.1134/S1061920825040065","DOIUrl":"10.1134/S1061920825040065","url":null,"abstract":"<p> For a hyperbolic semilinear partial differential equation, the problem of achieving a travelling wave is studied depending on the initial conditions. Numerical experiments show that the travelling wave structure depends on the rate of stabilization of the initial function at the leading edge. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"704 - 712"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Solarity of Deutsch Boundedly Compact Sets 德意志有界紧集的唯一性
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825040181
I.G. Tsar’kov
{"title":"Solarity of Deutsch Boundedly Compact Sets","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920825040181","DOIUrl":"10.1134/S1061920825040181","url":null,"abstract":"<p> Results on solarity of Deutsch boundedly compact sets are obtained. As application, we show that the set of extended exponential sums in <span>(C[a, b])</span> is a sun. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"827 - 832"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Coefficients of the Pearcey Function and Its Derivatives in a Representation of the Canonical Operator near a Cuspidal Caustic 关于正则算子在斜尖焦散附近的系数及其导数
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI: 10.1134/S1061920825040120
V.E. Nazaikinskii
{"title":"On the Coefficients of the Pearcey Function and Its Derivatives in a Representation of the Canonical Operator near a Cuspidal Caustic","authors":"V.E. Nazaikinskii","doi":"10.1134/S1061920825040120","DOIUrl":"10.1134/S1061920825040120","url":null,"abstract":"<p> In a neighborhood of a cuspidal caustic, the Maslov canonical operator can be represented as a linear combination of the composite Pearcey function and its derivatives with coefficients that are smooth functions independent of the small parameter of the asymptotics. This representation plays an important role when constructing asymptotic solutions of various equations describing wave propagation (such as the wave equation, Maxwell equations, and linearized shallow water equations). The paper provides a method for writing computationally efficient formulas for these coefficients, thus extending the preceding research in this direction. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 4","pages":"779 - 784"},"PeriodicalIF":1.5,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146043443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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