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Analysis of solutions of a second-order differential equation with impulsive delayed feedback 一类二阶脉冲时滞反馈微分方程解的分析
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090047
I. S. Kashchenko, I. N. Maslenikov
{"title":"Analysis of solutions of a second-order differential equation with impulsive delayed feedback","authors":"I. S. Kashchenko,&nbsp;I. N. Maslenikov","doi":"10.1134/S0040577926090047","DOIUrl":"10.1134/S0040577926090047","url":null,"abstract":"<p> We study the behavior of solutions to a nonlinear second-order differential equation with delay in the case where the feedback is of an impulsive type. The cases where the solutions of the linear part oscillate and do not oscillate are considered separately. In each case, the problem is reduced to studying the dynamics of a discrete mapping that is constructed explicitly. An analysis of the dynamical properties of the constructed mapping is performed, and the results are transferred to the original differential equation. It is shown that, depending on the parameters, the solution can monotonically tend to zero (starting from a certain moment of time) or tend to periodic or chaotic behavior. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1536 - 1552"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011465","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
Simplest solutions to the derivative nonlinear Schrödinger equation with integrable perturbation 具有可积摄动的微分非线性Schrödinger方程的最简解
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090126
A. O. Smirnov, A. S. Marchenko, A. A. Kaplieva
{"title":"Simplest solutions to the derivative nonlinear Schrödinger equation with integrable perturbation","authors":"A. O. Smirnov,&nbsp;A. S. Marchenko,&nbsp;A. A. Kaplieva","doi":"10.1134/S0040577926090126","DOIUrl":"10.1134/S0040577926090126","url":null,"abstract":"<p> We consider a hierarchy of integrable nonlinear equations depending on functions <span>(p)</span> and <span>(u)</span>. For <span>({uequiv0})</span>, this hierarchy transforms into the hierarchy of the derivative nonlinear Schrödinger equation. For <span>({unotequiv0})</span>, the constructed hierarchy equations describe the propagation of interacting nonlinear waves <span>(p)</span> and <span>(u)</span>. Some examples of solutions to the new integrable nonlinear equations are considered. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1675 - 1687"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011467","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 problem of front motion with a linear source in an external medium 在外部介质中具有线性源的锋面运动问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090059
N. T. Levashova
{"title":"The problem of front motion with a linear source in an external medium","authors":"N. T. Levashova","doi":"10.1134/S0040577926090059","DOIUrl":"10.1134/S0040577926090059","url":null,"abstract":"<p> The paper considers an initial-boundary value problem for a diffusion equation with modular nonlinearity. This problem was identified as a simplified formulation of a tumor growth model. In the present work, it was reduced to a single equation in the one-dimensional case. A distinctive feature of the problem is that the front is formed not between two saddle equilibrium positions, but between a saddle and a stable focus, or between a saddle and a stable node. The paper provides a justification for the existence of a solution to the model equation. The result of the study allows one to roughly estimate the velocity of the tumor propagation front, its dependence on the oxygen concentration, and the cell density in the proliferative layer. The methods employed in the study can be applied to a system of equations in the three-dimensional case for the purpose of justifying the general model. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1553 - 1564"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011460","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 Lie–Bianchi integrability of the full symmetric Toda system 全对称Toda系统的Lie-Bianchi可积性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090138
Yu. B. Chernyakov, G. I. Sharygin, D. V. Talalaev
{"title":"The Lie–Bianchi integrability of the full symmetric Toda system","authors":"Yu. B. Chernyakov,&nbsp;G. I. Sharygin,&nbsp;D. V. Talalaev","doi":"10.1134/S0040577926090138","DOIUrl":"10.1134/S0040577926090138","url":null,"abstract":"<p> We prove that the full symmetric Toda system is integrable in the sense of the Lie–Bianchi criterion. Specifically, we show that there exists a solvable Lie algebra of vector fields of dimension <span>(N=dim M)</span> on the phase space <span>(M)</span> of this system such that the system is invariant under the action of these fields. The proof is based on the symmetries of the full symmetric system constructed earlier, and the emergence of the stochastic Lie algebra structure in their description. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1688 - 1699"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011468","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
Homoclinic manifold splitting and Lyapunov landscape in a dissipative coupled nonlinear Schrödinger system 耗散耦合非线性Schrödinger系统中的同斜流形分裂和Lyapunov景观
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090102
V. M. Rothos
{"title":"Homoclinic manifold splitting and Lyapunov landscape in a dissipative coupled nonlinear Schrödinger system","authors":"V. M. Rothos","doi":"10.1134/S0040577926090102","DOIUrl":"10.1134/S0040577926090102","url":null,"abstract":"<p> We investigate the onset of deterministic spatiotemporal chaos in a weakly perturbed coupled nonlinear Schrödinger (CNLS) system that admits an explicit homoclinic breather in the Hamiltonian limit. Our analysis identifies a geometric mechanism organized by an internal <span>(1{:}1)</span> resonance near the symmetric equilibrium. A resonant amplitude-phase reduction reveals a two-scale spectral splitting that produces a one-dimensional unstable manifold persisting smoothly under perturbation. This codimension-one saddle structure allows homoclinic splitting to be characterized by an explicit scalar Melnikov function, whose zeros define a persistence surface in parameter space predicting transversal invariant-manifold intersections and chaotic transport. High-resolution numerical simulations, including maximal Lyapunov exponents, correlation-dimension estimates, and Poincaré sections, confirm that regions of enhanced Lyapunov instability align with the Melnikov persistence surface. The results provide a unified geometric interpretation of chaos in the perturbed CNLS system, showing that irregular dynamics is organized by resonant saddle geometry and global homoclinic splitting rather than by purely local linear instability. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1630 - 1652"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011463","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
Polynomial isomorphism of the family of parametric Korteweg–de Vries hierarchies 参数Korteweg-de Vries层次族的多项式同构
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090023
V. M. Buchstaber, E. Yu. Bunkova
{"title":"Polynomial isomorphism of the family of parametric Korteweg–de Vries hierarchies","authors":"V. M. Buchstaber,&nbsp;E. Yu. Bunkova","doi":"10.1134/S0040577926090023","DOIUrl":"10.1134/S0040577926090023","url":null,"abstract":"<p> A family of parametric Korteweg–de Vries hierarchies is introduced. For fixed values of the family parameters, the classical Korteweg–de Vries hierarchy is obtained, which has been described in terms of recursions in well-known works (Lenard, Gelfand–Dickey). A polynomial isomorphism is constructed between the studied family of parametric Korteweg–de Vries hierarchies and an explicitly defined sequence of infinite-dimensional polynomial dynamical systems. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1494 - 1512"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011464","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
Indices of some adjacencies of types (E_7) and (E_8) wavefront singularities (E_7)和(E_8)波前奇点类型的一些邻接索引
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090114
V. D. Sedykh
{"title":"Indices of some adjacencies of types (E_7) and (E_8) wavefront singularities","authors":"V. D. Sedykh","doi":"10.1134/S0040577926090114","DOIUrl":"10.1134/S0040577926090114","url":null,"abstract":"<p> We study simple stable wavefront singularities of a generic Legendrian map (e.g., for a wavefront propagation described by the eikonal equation in the cotangent bundle). The indices of adjacencies of singularities of types <span>(E_7)</span> and <span>(E_8)</span> to singularities whose preimages contain singular points of corank <span>(2)</span> are calculated. The calculations are based on the classification of singularities of the Legendrian germ of type <span>(E_mu)</span> that we obtain in this paper. Finally, we discuss the application of our results to the problem of classifying curves that appear as a result of small deformations of singular real curves in the plane. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1653 - 1674"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011466","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 chromatic and flow polynomials: Their combinatorics and physical applications 边界色多项式和流动多项式：它们的组合学和物理应用
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090035
A. A. Kazakov, E. Yu. Lerner, S. A. Mukhamedjanova
{"title":"Boundary chromatic and flow polynomials: Their combinatorics and physical applications","authors":"A. A. Kazakov,&nbsp;E. Yu. Lerner,&nbsp;S. A. Mukhamedjanova","doi":"10.1134/S0040577926090035","DOIUrl":"10.1134/S0040577926090035","url":null,"abstract":"<p> In this paper, we systematically study the properties of boundary analogs of the classical flow and chromatic polynomials: Whitney-type formulas, subgraph expansions, the combinatorial interpretation of their coefficients, and logarithmic concavity, as well as the duality of these polynomials. We demonstrate the connection between the obtained results and models of statistical physics, including Potts models, the Fortuin–Kasteleyn expansion, and flow models in the Biggs formalism. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1513 - 1535"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011470","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
Asymmetric boundary layers in a singularly perturbed reaction–diffusion–advection problem in a two-dimensional domain 二维奇异摄动反应-扩散-平流问题中的不对称边界层
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090084
A. O. Orlov, Xiong Zhuxuan, Li Zhiqiang, V. T. Volkov
{"title":"Asymmetric boundary layers in a singularly perturbed reaction–diffusion–advection problem in a two-dimensional domain","authors":"A. O. Orlov,&nbsp;Xiong Zhuxuan,&nbsp;Li Zhiqiang,&nbsp;V. T. Volkov","doi":"10.1134/S0040577926090084","DOIUrl":"10.1134/S0040577926090084","url":null,"abstract":"<p> We construct an asymptotic approximation of the solution of a singularly perturbed problem for a reaction–diffusion–advection equation in a strip. A distinctive feature of the problem is that it involves processes with disparate scales: superweak diffusion of the order of <span>(varepsilon^4)</span> and weak advection of the order of <span>(varepsilon)</span>. We establish that such a combination gives rise to qualitatively different boundary layers: a layer of width <span>(varepsilon^3)</span> is formed at one boundary of the strip, while a layer of width <span>(varepsilon)</span> is formed at the other. The asymptotic approximation of the solution is constructed by the boundary function method. The justification of the obtained approximation and the proof of the existence of a solution possessing the constructed asymptotics are carried out by means of the asymptotic method of differential inequalities, modified in accordance with the specific features of the problem. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1600 - 1612"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011472","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
Positon excitations in a higher-order Heisenberg ferromagnet 高阶海森堡铁磁体中的位置激发
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2026-09-22 DOI: 10.1134/S0040577926090096
R. U. Rahman, J. He, Z. Li
{"title":"Positon excitations in a higher-order Heisenberg ferromagnet","authors":"R. U. Rahman,&nbsp;J. He,&nbsp;Z. Li","doi":"10.1134/S0040577926090096","DOIUrl":"10.1134/S0040577926090096","url":null,"abstract":"<p> We study nonlinear magnetic excitations in a higher-order ferromagnetic system and identify weakly localized spin-wave modes beyond conventional magnetic solitons. Using the <span>(N)</span>-fold Darboux transformation (DT), explicit soliton and positon solutions are constructed on different ground-state backgrounds. While soliton solutions preserve the rotational symmetry of isotropic ferromagnets, positon solutions exhibit a slowly decaying oscillatory localization, representing a distinct type of spin-wave propagation. The structural and dynamical properties of these excitations are analyzed, revealing nontrivial magnetization profiles and the time-dependent phase evolution. Positon interactions are shown to be elastic, with excitations retaining their identities while experiencing nonconstant logarithmic phase shifts, in contrast to standard soliton scattering. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"228 3","pages":"1613 - 1629"},"PeriodicalIF":1.0,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011462","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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