Physica D: Nonlinear Phenomena最新文献_第8页

Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs 基于有向图的复球面上高维Kuramoto模型的指数同步

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134578

Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi

{"title":"Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs","authors":"Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi","doi":"10.1016/j.physd.2025.134578","DOIUrl":"10.1016/j.physd.2025.134578","url":null,"abstract":"<div><div>Synchronization of populations is a common phenomenon in nature. The high-dimensional Kuramoto model is one of the most typical continuous system models for studying synchronization phenomena in multi-individual systems. Due to Lohe’s remarkable work on models of multi-individual systems, the high-dimensional Kuramoto models are also called the Lohe models, and the Lohe Hermitian sphere (LHS) model is a generalization of the Lohe models in the complex space. In this paper, we study the exponential synchronization problem of the LHS models based on directed graphs. By introducing the synchronization error function, we have developed a set of synchronization error dynamic equations for the identical oscillators using matrix Riccati differential equations. The system of synchronization error dynamic equations is studied, a total error function is constructed, and exponential synchronization of the LHS model on the unit complex sphere is demonstrated. An approximate linearization of the error dynamics equations is performed, to obtain the exponential decay rate of the system. For the LHS model with nonidentical oscillators on the unit complex sphere, using the synchronization error function, it is shown that practical synchronization can be achieved when the connection graph of the system is strongly connected.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134578"},"PeriodicalIF":2.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On periodic solutions for the Maxwell–Bloch equations 麦克斯韦-布洛赫方程的周期解

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134581

A.I. Komech

引用次数: 0

On the nonexistence of NLS breathers 关于NLS呼吸者的不存在性

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-20 DOI: 10.1016/j.physd.2025.134580

Miguel Á. Alejo , Adán J. Corcho

引用次数: 0

Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model 碰撞破碎非线性聚集模型稳态解的存在性、稳定性及非线性估计

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-19 DOI: 10.1016/j.physd.2025.134579

Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha

{"title":"Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model","authors":"Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha","doi":"10.1016/j.physd.2025.134579","DOIUrl":"10.1016/j.physd.2025.134579","url":null,"abstract":"<div><div>Existence and uniqueness of a stationary-state solution to the nonlinear aggregation and collision-induced fragmentation equation is proved over a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-space. The assumption of a detailed balance condition is relaxed to attain the existence of the solution. Aggregation and fragmentation kernels are considered to exhibit linear and quadratic growth rates respectively which encompass a wide range of physically significant kernels. Asymptotic properties of the time-dependent solution are analyzed in detail and convergence of the same to the stationary-state solution is also examined. Exponential rate of convergence is obtained by proving the asymptotic stability of the stationary-state solution. Further, nonlinear estimates of the solution are obtained using semigroup theory of operators. The study is further extended to analyze the nonexistence of a stationary-state solution for a particular choice of kinetic kernels over a suitably constructed solution space. A numerical example is provided in order to visualize the nonexistence of a stationary-state solution and other physical quantities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134579"},"PeriodicalIF":2.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Breathers of the nonlinear Schrödinger equation are coherent self-similar solutions 非线性薛定谔方程的呼吸器是相干自相似解

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-17 DOI: 10.1016/j.physd.2025.134575

Alexey V. Slunyaev

引用次数: 0

Theoretical analysis of the effect of strength on oscillations and Rayleigh-Taylor instabilities on a collapsing spherical surface, supported by a study on Bell-Plesset oscillations 在Bell-Plesset振荡研究的支持下，对坍塌球面上强度对振荡和瑞利-泰勒不稳定性影响的理论分析

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-15 DOI: 10.1016/j.physd.2025.134588

C.A. Walsh

{"title":"Theoretical analysis of the effect of strength on oscillations and Rayleigh-Taylor instabilities on a collapsing spherical surface, supported by a study on Bell-Plesset oscillations","authors":"C.A. Walsh","doi":"10.1016/j.physd.2025.134588","DOIUrl":"10.1016/j.physd.2025.134588","url":null,"abstract":"<div><div>Small perturbations on a spherical interface, between two materials of different densities, oscillate in amplitude as the radius of the interface increases or decreases. The historical approach to this problem has been to solve Laplace's equation for the velocity potential in the domains on either side of the interface and equate the pressure at the interface. This paper considers the effects of yield strength and shear modulus on oscillations on a collapsing spherical surface between a higher density, strong material, and a lower-density, weak material.</div><div>The strong material is assumed to be incompressible, flow in an elasto-plastic manner and lie on the yield surface. The yield surface is taken to be defined by the von Mises yield criterion and the flow to follow the Prandtl-Reuss rules. The Navier-Stokes equation provides the starting point for the analysis and yields the necessary stress terms for inclusion in Laplace's equation. The analysis is limited to a first-order approximation. The material strength model is assumed to be constant. This paper will outline the theoretical analysis and show a comparison of the analytical results with simulations carried out using a hydrocode. The theoretical analysis will be shown to give good agreement with the calculations over a range of different initial wavelengths and strength parameters. When the yield strength is high, the amplitudes of the oscillations decay monotonically to zero; at even higher yield strengths oscillations are completely inhibited and the amplitudes increase, due to geometric convergence effects. Criteria for these phenomena are derived and shown to agree approximately with calculations made using the theoretical analysis.</div><div>UK Ministry of Defence © Crown Owned Copyright 2024/AWE</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134588"},"PeriodicalIF":2.7,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Whitham modulation theory for the discontinuous initial-value problem of the generalized Kaup–Boussinesq equation 广义kap - boussinesq方程不连续初值问题的Whitham调制理论

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-14 DOI: 10.1016/j.physd.2025.134573

Ruizhi Gong, Deng-Shan Wang

{"title":"Whitham modulation theory for the discontinuous initial-value problem of the generalized Kaup–Boussinesq equation","authors":"Ruizhi Gong, Deng-Shan Wang","doi":"10.1016/j.physd.2025.134573","DOIUrl":"10.1016/j.physd.2025.134573","url":null,"abstract":"<div><div>The Whitham modulation theory is developed to investigate the complete classification of solutions to discontinuous initial-value problem of the generalized Kaup–Boussinesq (KB) equation, which can model phenomenon of wave motion in shallow water. According to the dispersion relation, the generalized KB equation includes the generalized good-KB equation and generalized bad-KB equation, respectively. Firstly, the periodic wave solutions and the corresponding Whitham equations associated with the generalized bad-KB equation are given by Flaschka–Forest–McLaughlin approach. Secondly, the basic rarefaction wave structure and dispersive shock wave structure are described by analyzing the zero-genus and one-genus Whitham equations. Then the complete classification of solutions to Riemann problem of the generalized bad-KB equation is provided, and eighteen different cases are classified, including five critical cases. The distributions of Riemann invariants and the evolutions of self-similar states for each component are demonstrated in detail. It is shown that the exact soliton solution is in good agreement with the soliton edge of the modulated dispersive shock wave. Moreover, it is observed that the phase portraits in each case establish a consistent relationship with the behavior of the modulated solutions. Finally, for the generalized good-KB equation, a new type of discontinuous initial-value problem with constant-periodic wave boundaries is explored, and some novel modulated solutions with trigonometric shock waves are found. It is remarked that such trigonometric shock waves are absent in the generalized bad-KB equation because the small amplitude limits of the periodic waves are not trigonometric functions but constants. The results in this work reveal exotic wave-breaking phenomena in shallow water and provide a feasible way to investigate the discontinuous initial-value problem of nonlinear dispersive equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134573"},"PeriodicalIF":2.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Detecting imbalanced financial markets through time-varying optimization and nonlinear functionals 通过时变优化和非线性函数检测失衡的金融市场

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-13 DOI: 10.1016/j.physd.2025.134571

Nick James , Max Menzies

引用次数: 0

Shock selection in reaction–diffusion equations with partially negative diffusivity using nonlinear regularisation 部分负扩散方程中激波选择的非线性正则化

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-12 DOI: 10.1016/j.physd.2025.134561

Thomas Miller , Alexander K.Y. Tam , Robert Marangell , Martin Wechselberger , Bronwyn H. Bradshaw-Hajek

{"title":"Shock selection in reaction–diffusion equations with partially negative diffusivity using nonlinear regularisation","authors":"Thomas Miller , Alexander K.Y. Tam , Robert Marangell , Martin Wechselberger , Bronwyn H. Bradshaw-Hajek","doi":"10.1016/j.physd.2025.134561","DOIUrl":"10.1016/j.physd.2025.134561","url":null,"abstract":"<div><div>Solutions to reaction–nonlinear-diffusion (RND) equations with a region of negative diffusivity exhibit shocks. In general, the position of these shocks can vary, necessitating selection criteria to determine a unique shock. Previous studies have defined conditions for shock selection. A common choice is the equal area rule, which corresponds to a fourth-order non-local regularisation to the RND equation. Bradshaw-Hajek et al. (2024) showed that combining non-local and viscous regularisations can yield a continuum of possible shocks. In this work, we demonstrate how to achieve a continuum of shocks using a single nonlinear regularisation term. With one nonlinear regularisation, shock selection obeys a modified equal area rule, where adjusting the nonlinearity in the regularisation moves the shock. To demonstrate the technique, we attain solutions with conserved diffusivity across the shock, which yield the longest shock length possible. Using geometric singular perturbation theory, we prove the existence of travelling waves with continuous diffusivity shocks. Numerical solutions align with theoretical predictions for shock position and wave speed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134561"},"PeriodicalIF":2.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quasi-periodic swing via weak KAM theory 弱KAM理论拟周期摆动

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-12 DOI: 10.1016/j.physd.2025.134559

Xun Niu , Kaizhi Wang , Yong Li

引用次数: 0