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Localized structures in a saturable discrete NLS equation with next-nearest-neighbor interactions 具有次近邻相互作用的饱和离散NLS方程的局域结构
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070141
V. M. Rothos
{"title":"Localized structures in a saturable discrete NLS equation with next-nearest-neighbor interactions","authors":"V. M. Rothos","doi":"10.1134/S0040577925070141","DOIUrl":"10.1134/S0040577925070141","url":null,"abstract":"<p> We address the existence of solitons and periodic traveling-wave solutions in a saturable discrete NLS (dNLS) equation with next-nearest-neighbor interactions. Calculus of variations and Nehari manifolds are employed to establish the existence of discrete solitons. We prove the existence of periodic traveling waves studying the mixed-type functional differential equations using Palais–Smale conditions and variational methods. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1280 - 1294"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144681","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
Self-distributive algebras and bialgebras 自分配代数与双代数
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070013
V. G. Bardakov, T. A. Kozlovskaya, D. V. Talalaev
{"title":"Self-distributive algebras and bialgebras","authors":"V. G. Bardakov,&nbsp;T. A. Kozlovskaya,&nbsp;D. V. Talalaev","doi":"10.1134/S0040577925070013","DOIUrl":"10.1134/S0040577925070013","url":null,"abstract":"<p> We study self-distributive algebraic structures: algebras, bialgebras, additional structures on them, relations of these structures with Hopf algebras, Lie algebras, Leibnitz algebras, etc. The basic example of such structures is given by rack and quandle bialgebras. But we go further to the general coassociative comultiplication. The principal motivation for this work is the development of linear algebra related to the notion of a quandle in analogy with the ubiquitous role of group algebras in the category of groups with possible applications to the theory of knot invariants. We describe self-distributive algebras and show that some quandle algebras and some Novikov algebras are self-distributive. We also give a full classification of counital self-distributive bialgebras in dimension <span>(2)</span> over <span>(mathbb{C})</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1103 - 1118"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144623","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
Modular-type nonlinearity in the modeling of tumor spheroid growth 肿瘤球体生长模型中的模型非线性
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070086
N. T. Levashova, E. A. Generalov, A. E. Sidorova, A. N. Goltsov
{"title":"Modular-type nonlinearity in the modeling of tumor spheroid growth","authors":"N. T. Levashova,&nbsp;E. A. Generalov,&nbsp;A. E. Sidorova,&nbsp;A. N. Goltsov","doi":"10.1134/S0040577925070086","DOIUrl":"10.1134/S0040577925070086","url":null,"abstract":"<p> A space–time trigger model of tumor growth is considered depending on the concentration of hydrogen ions, oxygen, and tumor cell density at the initial stage of the tumor spheroid development. A system of parabolic equations with a piecewise linear right-hand side of modular type is used to solve this problem. Numerical implementation is carried out in a three-dimensional domain shaped as a cube with an edge of 0.1 mm on a uniform grid using the method of lines, the Rosenbrock scheme, and the factorization method in the spatial coordinates. The presented model quite well describes the dynamics of variation in the spheroid area at the initial stage of the tumor development depending on time. A distinctive feature of the model is that it reflects both the process of tumor growth into the external environment and the formation of a necrotic core at the tumor center. Based on the presented system of equations, it is possible to design a model that takes both the heterogeneity of the environment and more complex mechanisms of tumorigenesis into account. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1202 - 1210"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144622","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 elliptic lattice KdV system revisited 对椭圆点阵KdV体系的再考察
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070116
F. W. Nijhoff, C. Zhang, D.-J. Zhang
{"title":"The elliptic lattice KdV system revisited","authors":"F. W. Nijhoff,&nbsp;C. Zhang,&nbsp;D.-J. Zhang","doi":"10.1134/S0040577925070116","DOIUrl":"10.1134/S0040577925070116","url":null,"abstract":"<p> The elliptic lattice KdV system, discovered in 2003, is an extension of the lattice potential KdV equation associated with an elliptic curve. This is a rather complicated three-component system on the quad lattice, which contains the moduli of the elliptic curve as parameters. In this paper, we investigate this system further and, among other results, derive a two-component multiquartic form of the system on the quad lattice. Furthermore, we construct an elliptic Yang–Baxter map and study the associated continuous and semidiscrete systems. In particular, we derive the so-called “generating PDE” for this system, comprising a six-component system of second-order PDEs, which can be considered to constitute an elliptic extension of the Ernst equations of General Relativity. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1234 - 1256"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144663","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
From NLS-type matrix refactorization problems to set-theoretic solutions of the 2- and 3-simplex equations 从nls型矩阵重构问题到2和3单形方程的集论解
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070050
S. Konstantinou-Rizos
{"title":"From NLS-type matrix refactorization problems to set-theoretic solutions of the 2- and 3-simplex equations","authors":"S. Konstantinou-Rizos","doi":"10.1134/S0040577925070050","DOIUrl":"10.1134/S0040577925070050","url":null,"abstract":"<p> We present a method for constructing hierarchies of solutions of <span>(n)</span>-simplex equations by varying the spectral parameter in their Lax representation. We use this method to derive new solutions of the set-theoretic <span>(2)</span>- and <span>(3)</span>-simplex equations that are related to the Adler map and nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang–Baxter maps are completely integrable. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1154 - 1166"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144679","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
Irregular dynamics of internal waves in a weakly stratified fluid in the viscous Benjamin–Ono equation model 粘性Benjamin-Ono方程模型中弱分层流体内波的不规则动力学
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070037
M. V. Flamarion, E. Pelinovsky
{"title":"Irregular dynamics of internal waves in a weakly stratified fluid in the viscous Benjamin–Ono equation model","authors":"M. V. Flamarion,&nbsp;E. Pelinovsky","doi":"10.1134/S0040577925070037","DOIUrl":"10.1134/S0040577925070037","url":null,"abstract":"<p> We investigate the complex dynamics of narrow-band wave fields described by the viscous Benjamin–Ono equation, a model of significant relevance in hydrodynamics. Through detailed numerical simulations, we analyze the role of Reynolds viscosity in shaping statistical moments, energy spectra, and the occurrence of extreme internal wave events. In particular, we show that freak waves of moderate amplitude can occur in viscous fluids. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1126 - 1135"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144678","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 the reaction–diffusion problem in the case of a balance between reaction and diffusion 在反应扩散平衡的情况下，反应扩散问题中的锋面运动
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070128
A. O. Orlov, A. R. Makhmudov
{"title":"Front motion in the reaction–diffusion problem in the case of a balance between reaction and diffusion","authors":"A. O. Orlov,&nbsp;A. R. Makhmudov","doi":"10.1134/S0040577925070128","DOIUrl":"10.1134/S0040577925070128","url":null,"abstract":"<p> We show the existence and uniqueness of the solution with a moving internal transition layer in the initial boundary-value problem for the singularly perturbed parabolic reaction–diffusion equation in the case of a balance between reaction and diffusion. Using the Vasil’eva method of boundary functions, we construct an asymptotic approximation of the solution of the front form. We prove the existence and uniqueness theorem using the asymptotic method of Nefedov’s differential inequalities. The obtained results can be used to develop effective numerical algorithms for solving hard problems appearing in the theory of nonlinear heat conduction and in population dynamics. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1257 - 1270"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144664","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
Error estimates of the Galerkin method for a weakly solvable parabolic equation with a nonlocal-in-time condition for the solution 具有非局部时条件的弱可解抛物方程Galerkin方法的误差估计
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070025
A. S. Bondarev, A. A. Petrova, O. M. Pirovskikh
{"title":"Error estimates of the Galerkin method for a weakly solvable parabolic equation with a nonlocal-in-time condition for the solution","authors":"A. S. Bondarev,&nbsp;A. A. Petrova,&nbsp;O. M. Pirovskikh","doi":"10.1134/S0040577925070025","DOIUrl":"10.1134/S0040577925070025","url":null,"abstract":"<p> We consider the abstract linear parabolic equation with a nonlocal-in-time condition for an integral-type solution in a separable Hilbert space. The problem is solved approximately using the semidiscrete Galerkin method. Under conditions of weak solvability for the problem, we establish error estimates for an approximate solution. Under additional assumptions on the smoothness of the solution of the exact problem, we also obtain the convergence rate that is exact in the order of approximation for projection subspaces of finite-element type. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1119 - 1125"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145121","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
Using the Kantorovich–Galerkin approach to analyze the resonant characteristics of damped systems 用Kantorovich-Galerkin方法分析了阻尼系统的谐振特性
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-07-25 DOI: 10.1134/S0040577925070098
V. L. Litvinov, K. V. Litvinova
{"title":"Using the Kantorovich–Galerkin approach to analyze the resonant characteristics of damped systems","authors":"V. L. Litvinov,&nbsp;K. V. Litvinova","doi":"10.1134/S0040577925070098","DOIUrl":"10.1134/S0040577925070098","url":null,"abstract":"<p> The Kantorovich–Galerkin method is extended to solve a wider range of problems related to oscillations of mechanical systems with moving boundaries. We take bending rigidity, environmental resistance, and foundation rigidity into account. The main attention is paid to studying the resonance characteristics of the solutions obtained. Quadrature expressions for the amplitudes of dynamical modes of different orders are derived. As an illustration, the problem of forced oscillations of a string with a uniformly moving boundary is considered. The error of the Kantorovich–Galerkin method is estimated depending on the velocity of the boundaries. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"224 1","pages":"1211 - 1219"},"PeriodicalIF":1.1,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144624","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
Hall current and MHD impacts on a 3D Maxwell nanofluid flow across a porous stretching surface 霍尔电流和MHD对通过多孔拉伸表面的三维麦克斯韦纳米流体流动的影响
IF 1.1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2025-06-25 DOI: 10.1134/S0040577925060030
G. Murali, J. Venkata Madhu, G. Deepa, P. Suresh, S. K. Nuslin
{"title":"Hall current and MHD impacts on a 3D Maxwell nanofluid flow across a porous stretching surface","authors":"G. Murali,&nbsp;J. Venkata Madhu,&nbsp;G. Deepa,&nbsp;P. Suresh,&nbsp;S. K. Nuslin","doi":"10.1134/S0040577925060030","DOIUrl":"10.1134/S0040577925060030","url":null,"abstract":"<p> The purpose of this study is to investigate the influence that heat radiation has on the flow of a three-dimensional, viscous, electrically conducting, incompressible, upper-convicted Maxwell nanofluid over a bidirectional stretching surface. Additionally, aspects such as magnetic fields, porous media, thermophoresis, and Brownian motion are taken into consideration. Nonlinear radiative heat transmission is included in the energy equation in the Rosseland approximation version of the equation. For the purpose of resolving the ordinary differential equations that are formed from the reduction of the main governing nonlinear partial differential equations by similarity transformations, the “bvp4c” solver by MATLAB is used. The skin-friction, heat transfer rates, and mass transfer coefficients are analyzed numerically, and visual representations are used to demonstrate the impacts of a large number of important components on the velocity, temperature, and concentration profiles. The numerical findings of the study have been evaluated, and it has been determined that they are substantially in accord with the results available in the literature. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"223 3","pages":"899 - 914"},"PeriodicalIF":1.1,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144686","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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