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Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities 具有 KPZ 非线性的快速和慢速反应-扩散-对流方程系统中带有边界层的静态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 : 2024-07-27 DOI: 10.1134/S0040577924070092
N. N. Nefedov, A. O. Orlov
{"title":"Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities","authors":"N. N. Nefedov,&nbsp;A. O. Orlov","doi":"10.1134/S0040577924070092","DOIUrl":"10.1134/S0040577924070092","url":null,"abstract":"<p> The existence of stationary solutions of singularly perturbed systems of reaction–diffusion–advection equations is studied in the case of fast and slow reaction–diffusion–advection equations with nonlinearities containing the gradient of the squared sought function (KPZ nonlinearities). The asymptotic method of differential inequalities is used to prove the existence theorems. The boundary layer asymptotics of solutions are constructed in the case of Neumann and Dirichlet boundary conditions. The case of quasimonotone sources and systems without the quasimonotonicity requirement is also considered. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1178 - 1192"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775693","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
Boundary control problem for the reaction– advection– diffusion equation with a modulus discontinuity of advection 具有模量不连续平流的反应-平流-扩散方程的边界控制问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070043
P. E. Bulatov, Han Cheng, Yuxuan Wei, V. T. Volkov, N. T. Levashova
{"title":"Boundary control problem for the reaction– advection– diffusion equation with a modulus discontinuity of advection","authors":"P. E. Bulatov,&nbsp;Han Cheng,&nbsp;Yuxuan Wei,&nbsp;V. T. Volkov,&nbsp;N. T. Levashova","doi":"10.1134/S0040577924070043","DOIUrl":"10.1134/S0040577924070043","url":null,"abstract":"<p> We consider a periodic problem for a singularly perturbed parabolic reaction–diffusion–advection equation of the Burgers type with the modulus advection; it has a solution in the form of a moving front. We formulate conditions for the existence of such a solution and construct its asymptotic approximation. We pose a control problem where the required front propagation law is implemented by a specially chosen boundary condition. We construct an asymptotic solution of the boundary control problem. Using the asymptotic method of differential inequalities, we estimate the accuracy of the solution of the control problem. We propose an original numerical algorithm for solving singularly perturbed problems involving the modulus advection. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1097 - 1109"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775696","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 contrast structures in a problem of the baretting effect theory 关于裸丁效应理论问题中的对比结构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070109
E. I. Nikulin, V. T. Volkov, A. G. Nikitin
{"title":"On contrast structures in a problem of the baretting effect theory","authors":"E. I. Nikulin,&nbsp;V. T. Volkov,&nbsp;A. G. Nikitin","doi":"10.1134/S0040577924070109","DOIUrl":"10.1134/S0040577924070109","url":null,"abstract":"<p> We obtain a contrast-structure type solution of a system of equations for the baretting effect that include a nonlinear singularly perturbed parabolic equation and an additional nonlocal integral relation. We prove the existence of the solution with an internal transition layer and construct the asymptotic approximation of this solution. We obtain estimates of the main physical model parameters, which coincide with experimental data and the estimates obtained previously by other methods. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1193 - 1200"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775695","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
(n)-valued quandles and associated bialgebras $$n$$ 有值准绳和相关双贝叶斯
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070031
V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev
{"title":"(n)-valued quandles and associated bialgebras","authors":"V. G. Bardakov,&nbsp;T. A. Kozlovskaya,&nbsp;D. V. Talalaev","doi":"10.1134/S0040577924070031","DOIUrl":"10.1134/S0040577924070031","url":null,"abstract":"<p> We study <span>(n)</span>-valued quandles and <span>(n)</span>-corack bialgebras. These structures are closely related to topological field theories in dimensions <span>(2)</span> and <span>(3)</span>, to the set-theoretic Yang–Baxter equation, and to the <span>(n)</span>-valued groups, which have attracted considerable attention or researchers. We elaborate the basic methods of this theory, find an analogue of the so-called coset construction known in the theory of <span>(n)</span>-valued groups, and construct <span>(n)</span>-valued quandles using <span>(n)</span>-multiquandles. In contrast to the case of <span>(n)</span>-valued groups, this construction turns out to be quite rich in algebraic and topological applications. We study the properties of <span>(n)</span>-corack bialgebras, which play a role similar to that of bialgebras in group theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1080 - 1096"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775689","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
Singularities of 3D vector fields preserving the Martinet form 保留马丁内特形式的三维矢量场的奇异性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070018
S. Anastassiou
{"title":"Singularities of 3D vector fields preserving the Martinet form","authors":"S. Anastassiou","doi":"10.1134/S0040577924070018","DOIUrl":"10.1134/S0040577924070018","url":null,"abstract":"<p> We study the local structure of vector fields on <span>(mathbb{R}^3)</span> that preserve the Martinet <span>(1)</span>-form <span>(alpha=(1+x)dypm z,dz)</span>. We classify their singularities up to diffeomorphisms that preserve the form <span>(alpha)</span>, as well as their transverse unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1061 - 1069"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775686","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
Finite-gap solutions of the real modified Korteweg–de Vries equation 实修正科特韦格-德-弗里斯方程的有限间隙解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070122
A. O. Smirnov, I. V. Anisimov
{"title":"Finite-gap solutions of the real modified Korteweg–de Vries equation","authors":"A. O. Smirnov,&nbsp;I. V. Anisimov","doi":"10.1134/S0040577924070122","DOIUrl":"10.1134/S0040577924070122","url":null,"abstract":"<p> We consider methods for constructing finite-gap solutions of the real classical modified Korteweg–de Vries equation and elliptic finite-gap potentials of the Dirac operator. The Miura transformation is used in both methods to relate solutions of the Korteweg–de Vries and modified Korteweg–de Vries equations. We present examples. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1224 - 1240"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775698","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
Adiabatic perturbation theory for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions 具有非消失边界条件的矢量非线性薛定谔方程的绝热扰动理论
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070110
V. M. Rothos
{"title":"Adiabatic perturbation theory for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions","authors":"V. M. Rothos","doi":"10.1134/S0040577924070110","DOIUrl":"10.1134/S0040577924070110","url":null,"abstract":"<p> We consider a defocusing Manakov system (vector nonlinear Schrödinger (NLS) system) with nonvanishing boundary conditions and use the inverse scattering transform formalism. Integrable models provide a very useful proving ground for testing new analytic and numerical approaches to studying the vector NLS system. We develop a perturbation theory for the integrable vector NLS model. Evidently, small disturbance of the integrability condition can be considered a perturbation of the integrable model. Our formalism is based on the Riemann–Hilbert problem associated with the vector NLS model with nonvanishing boundary conditions. We use the RH and adiabatic perturbation theory to analyze the dynamics of dark–dark and dark–bright solitons in the presence of a perturbation with nonvanishing boundary conditions. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1201 - 1223"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775697","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
Stabilization of the front in a medium with discontinuous characteristics 在具有不连续特性的介质中稳定前沿
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070079
N. T. Levashova, E. A. Chunzhuk, A. O. Orlov
{"title":"Stabilization of the front in a medium with discontinuous characteristics","authors":"N. T. Levashova,&nbsp;E. A. Chunzhuk,&nbsp;A. O. Orlov","doi":"10.1134/S0040577924070079","DOIUrl":"10.1134/S0040577924070079","url":null,"abstract":"<p> We study the autowave front propagation in a medium with discontinuous characteristics and the conditions for its stabilization to a stationary solution with a large gradient at the interface between media in the one-dimensional case. The asymptotic method of differential inequalities, based on constructing an asymptotic approximation of the solution, is the main method of study. We develop an algorithm for constructing such an approximation for the solution of the moving front form in a medium with discontinuous characteristics. The application of such an algorithm requires a detailed analysis of the behavior of the solution in neighborhoods of two singular points: the front localization point and the medium discontinuity point. As a result, we obtain a system of equations for the front propagation speed; this distinguishes this paper from the previously published ones. The developed algorithm can be used to describe autowave propagation in layered media. The results can also be extended to the multidimensional case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1139 - 1156"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775761","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
Triple equivalence of the oscillatory behavior for scalar delay differential equations 标量延迟微分方程振荡行为的三重等价性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI: 10.1134/S0040577924070080
P. N. Nesterov, J. I. Stavroulakis
{"title":"Triple equivalence of the oscillatory behavior for scalar delay differential equations","authors":"P. N. Nesterov,&nbsp;J. I. Stavroulakis","doi":"10.1134/S0040577924070080","DOIUrl":"10.1134/S0040577924070080","url":null,"abstract":"<p> We study the oscillation of a first-order delay equation with negative feedback at the critical threshold <span>(1/e)</span>. We apply a novel center manifold method, proving that the oscillation of the delay equation is equivalent to the oscillation of a <span>(2)</span>-dimensional system of ordinary differential equations (ODEs) on the center manifold. It is well known that the delay equation oscillation is equivalent to the oscillation of a certain second-order ODE, and we furthermore show that the center manifold system is asymptotically equivalent to this same second-order ODE. In addition, the center manifold method has the advantage of being applicable to the case where the parameters oscillate around the critical value <span>(1/e)</span>, thereby extending and refining previous results in this case. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"220 1","pages":"1157 - 1177"},"PeriodicalIF":1.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775694","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
Erratum to: On the existence of certain elliptic solutions of the cubically nonlinear Schrödinger equation 勘误：论立方非线性薛定谔方程的某些椭圆解的存在性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI: 10.1134/S0040577924060126
H. W. Schürmann, V. S. Serov
{"title":"Erratum to: On the existence of certain elliptic solutions of the cubically nonlinear Schrödinger equation","authors":"H. W. Schürmann,&nbsp;V. S. Serov","doi":"10.1134/S0040577924060126","DOIUrl":"10.1134/S0040577924060126","url":null,"abstract":"","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"219 3","pages":"1060 - 1060"},"PeriodicalIF":1.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413684","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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