非线性科学

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[1] arXiv:2510.17806 [中文pdf, pdf, html, 其他]

标题： 一般分数阶动力学 显示英文标题

标题： General Fractional Dynamics

Vasily E. Tarasov

评论： 39页。LaTeX

期刊参考： 数学。2021年。第9卷。第13期。文章编号1464

主题： 混沌动力学 (nlin.CD) ; 动力系统 (math.DS)

广义分数阶动力学（GFDynamics）可以被视为一门交叉科学，其中通过使用广义分数阶微积分、包含广义分数阶积分（GFI）和导数（GFD）的方程，或具有离散时间的广义非局部映射，研究线性和非线性动力系统中的非局部特性。 GFDynamics意味着研究和获得关于非局部性一般形式的结果，这些结果可以通过一般形式的算子核来描述，而不是其特定的实现和表示。 在本文中，提出了“广义非局部映射”的概念，这些是离散点上包含GFI和GFD方程的精确解。 在这些映射中，非局部性由与初始方程中使用的广义分数阶积分和导数的Sonin和Luchko核相关的核决定。 利用广义分数阶微积分，我们考虑了时间上具有广义非局部性的分数阶系统，这些系统由包含广义分数阶算子和周期性冲击的方程描述。 任意阶的GFI和GFD方程也用于推导广义非局部映射。 获得了带有冲击的这些广义分数阶微分和积分方程的精确解。 这些具有离散时间点的精确解被用来推导无需近似的广义非局部映射。 描述了时间非局部性的某些例子。 显示英文摘要

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the non-local properties of linear and nonlinear dynamical systems are studied by using of general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. The GFDynamics implies research and obtaining results concerning of general form of nonlocality, which can be described by general form operator kernels, and not its particular implementations and representations. In this paper, it is proposed the concept of "general nonlocal maps" that are exact solutions of equations with GFI and GFD at discrete points. In these maps, the non-locality is determined by the kernels that are associated to the Sonin and Luchko kernels of general fractional integrals and derivatives, which are used in initial equations. Using general fractional calculus, we consider fractional systems with general non-locality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order are also used to derive general nonlocal maps. Exact solutions for these general fractional differential and integral equations with kicks are obtained. These exact solutions with discrete time points are used to derive general nonlocal maps without approximations. Some examples of non-locality in time are described.

[2] arXiv:2510.17819 [中文pdf, pdf, html, 其他]

标题： 分形结构上的非线性克莱因-戈登方程的扭结-反扭结孤子解 显示英文标题

标题： Kink-antikink soliton solutions of the nonlinear Klein-Gordon equation on branched structures

Q.U.Asadov, K.K.Sabirov, J.R.Yusupov

主题： 模式形成与孤子 (nlin.PS) ; 精确可解与可积系统 (nlin.SI)

在本文中，我们研究具有三个半无限边的度量星图上的非线性克莱因-戈登方程。 在分支点，我们施加加权连续性条件和广义加权基尔霍夫条件，用于波函数导数。 通过采用分析方法和数值技术，我们构建了满足顶点条件并保持能量和动量守恒的精确和数值孤子解。 分析计算的结果通过数值实验得到验证，这些实验展示了kink-antikink孤子解的无反射传播。 我们计算并分析了反射系数，研究了各种非线性参数的影响，并进一步将该公式扩展到其他图拓扑结构，如树图和环图。 显示英文摘要

In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity condition and a generalized weighted Kirchhoff condition for the derivatives of the wave function. By employing both analytical methods and numerical techniques, we construct exact and numerical soliton solutions that satisfy the vertex conditions and conserve energy and momentum. The results of analytic calculations are confirmed through numerical experiments, which demonstrate reflectionless propagation of kink-antikink soliton solutions. We compute and analyze the reflection coefficient, study the impact of various nonlinearity parameters, and further extend the formulation to other graph topologies, such as tree and loop graphs.

[3] arXiv:2510.18580 [中文pdf, pdf, html, 其他]

标题： 从双曲到非双曲开放弹球：熵与标度律方法 显示英文标题

标题： From Hyperbolic to Non-Hyperbolic Open Billiards: An Entropy and Scaling Law Approach

P. Haerter, A. F. Bosio, E. D. Leonel, M.A.F. Sanjuán, R. L. Viana

主题： 混沌动力学 (nlin.CD)

我们研究在均匀重力场影响下的开放圆形弹道中的逃逸动力学。 系统特性作为粒子总能量和边界上两个对称放置的孔的大小的函数进行研究。 使用一系列定量工具，包括逃逸盆地、盆地熵（$S_b$）、平均逃逸时间（$\bar{\tau}$）和生存概率（$P(n)$），我们描述了一个从低能区的完全混沌、双曲区域过渡到高能区的非双曲、混合相空间的系统。 我们的结果表明，这种转变由科莫戈罗夫-阿诺德-莫泽（KAM）岛的出现所标志。 我们证明盆地熵和平均逃逸时间都对该转变敏感，前者在粘滞KAM岛出现时达到峰值，后者则急剧增加。 生存概率分析证实了这一动力学图景，在双曲区域中呈现纯指数衰减，在混合区域中则呈现幂律类似衰减并伴有饱和平台，这直接量化了被困轨道的测度。 在高能极限下，系统动力学趋于可积情况，导致通过$S_b$和$\bar{\tau}$测量的复杂性相应降低。 显示英文摘要

We investigate the escape dynamics in an open circular billiard under the influence of a uniform gravitational field. The system properties are investigated as a function of the particle total energy and the size of two symmetrically placed holes in the boundary. Using a suite of quantitative tools including escape basins, basin entropy ($S_b$), mean escape time ($\bar{\tau}$), and survival probability ($P(n)$), we characterize a system that transitions from a fully chaotic, hyperbolic regime at low energies to a non-hyperbolic, mixed phase space at higher energies. Our results demonstrate that this transition is marked by the emergence of Kolmogorov-Arnold-Moser (KAM) islands. We show that both the basin entropy and the mean escape time are sensitive to this transition, with the former peaking and the latter increasing sharply as the sticky KAM islands appear. The survival probability analysis confirms this dynamical picture, shifting from a pure exponential decay in the hyperbolic regime to a power-law-like decay with a saturation plateau in the mixed regime, which directly quantifies the measure of trapped orbits. In the high-energy limit, the system dynamics approaches an integrable case, leading to a corresponding decrease in complexity as measured by both $S_b$ and $\bar{\tau}$.

交叉提交 (展示 4 之 4 条目 )

[4] arXiv:2510.17810 (交叉列表自 eess.SP) [中文pdf, pdf, html, 其他]

标题： 探索疾病心电图信号中的复杂性变化以提高分类性能 显示英文标题

标题： Exploring Complexity Changes in Diseased ECG Signals for Enhanced Classification

Camilo Quiceno Quintero, Sandip Varkey George

评论： 提交至NODYCON 2025的版本

主题： 信号处理 (eess.SP) ; 机器学习 (cs.LG) ; 混沌动力学 (nlin.CD) ; 数据分析、统计与概率 (physics.data-an)

心脏的复杂动力学反映在其电活动上，通过心电图（ECGs）捕捉。 在本研究中，我们使用非线性时间序列分析来理解ECG复杂性如何随着心脏病理变化而变化。 使用大型PTB-XL数据集，我们从导联II的ECGs中提取非线性度量，并使用Spearman相关性和互信息提取跨通道度量（导联II、V2、AVL）。 在几乎所有度量中，患病个体和健康个体之间以及5个诊断 superclass（$p<.001$）之间均发现了显著差异。 此外，将这些复杂性量化器纳入机器学习模型显著提高了分类准确率，使用ROC曲线下的面积（AUC）测量，从0.86（基线）提高到0.87（非线性度量）以及0.90（包括跨时间序列度量）。 显示英文摘要

The complex dynamics of the heart are reflected in its electrical activity, captured through electrocardiograms (ECGs). In this study we use nonlinear time series analysis to understand how ECG complexity varies with cardiac pathology. Using the large PTB-XL dataset, we extracted nonlinear measures from lead II ECGs, and cross-channel metrics (leads II, V2, AVL) using Spearman correlations and mutual information. Significant differences between diseased and healthy individuals were found in almost all measures between healthy and diseased classes, and between 5 diagnostic superclasses ($p<.001$). Moreover, incorporating these complexity quantifiers into machine learning models substantially improved classification accuracy measured using area under the ROC curve (AUC) from 0.86 (baseline) to 0.87 (nonlinear measures) and 0.90 (including cross-time series metrics).

[5] arXiv:2510.17964 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]

标题： 涡旋-反涡旋碰撞中的共振现象 显示英文标题

标题： Resonance phenomena in vortex-antivortex collisions

Maximilian Bachmaier, Andrzej Wereszczynski

评论： 9页，7图，1个附加视频：https://youtu.be/1o__huMd13o

主题： 高能物理 - 理论 (hep-th) ; 高能物理 - 现象学 (hep-ph) ; 模式形成与孤子 (nlin.PS)

在本工作中，我们提供了尼尔森-奥利弗斯涡旋与反涡旋之间散射场景的完整图谱。 重要的是，在深度II型 regime 中，这种碰撞揭示了最终状态形成中的混沌模式，其中弹回窗口被嵌入到湮灭区域中。 这种结构是由于由涡旋所承载的准正则模态引发的能量转移机制，特别是费什巴赫共振模态。 显示英文摘要

In this work, we provide a full map of scattering scenarios between a Nielsen-Olesen vortex and antivortex. Importantly, in the deep type II regime, such a collision reveals a chaotic pattern in the final state formation with bounce windows immersed into annihilation regions. This structure is due to the energy transfer mechanism triggered by a quasinormal mode, specifically the Feshbach resonant mode, hosted by the vortex.

[6] arXiv:2510.18349 (交叉列表自 math.SP) [中文pdf, pdf, html, 其他]

标题： 关于一维PT对称周期薛定谔算子谱的扰动 显示英文标题

标题： On perturbations of the spectrum of one-dimensional PT-symmetric periodic Schrodinger operator

P.G. Grinevich, I.A. Taimanov

评论： 8页

主题： 谱理论 (math.SP) ; 数学物理 (math-ph) ; 精确可解与可积系统 (nlin.SI)

对于PT对称的周期性薛定谔算子，它是零势能的小扰动，我们在微扰理论的领先阶计算谱和布洛赫函数零点的除子。 特别地，我们证明布洛赫谱的间隙的类似物是椭圆，它们的焦点与谱曲线的分支点重合。 显示英文摘要

For PT-symmetric periodic Schrodinger operator, which is a small perturbation of the zero potential, we calculate the spectrum and the divisor of zeroes of the Bloch function in the leading order of the perturbation theory. In particular, we show that the analogs of lacunae of the Bloch spectrum are ellipses, and their focal points coincide with the branch points of the spectral curve.

[7] arXiv:2510.18472 (交叉列表自 physics.optics) [中文pdf, pdf, html, 其他]

标题： 计算物理在光子器件中的应用 显示英文标题

标题： Computational Physics Applied to Photonic Devices

Gian-Luca Oppo

评论： 86页，41图

主题： 光学 (physics.optics) ; 模式形成与孤子 (nlin.PS)

我们都知道，第一台激光装置是由西奥多·梅曼于1960年在休斯实验室实现的。 较少为人所知的是，梅曼激光器显示的弛豫振荡的计算机模拟也是在1960年使用数字IBM 704计算机进行的。 原因是激光器和几乎所有光子器件都由非线性方程描述，这些方程往往无法在纸上解析求解。 从那时起，激光器和光子器件的发展与计算机模拟和数值编程的进步同步进行。 在本文综述中，我们介绍并数值求解了多种器件的模型方程，包括激光器、参数调制的激光器、注入式激光器、克尔谐振器、可饱和吸收体和光学参量振荡器。 通过使用计算机模拟，我们通过分叉、鞍点-节点分叉、霍普夫分叉和图灵分叉展示了这些光子器件中非线性解的稳定性和不稳定性；双稳态、非线性振荡、确定性混沌、图灵图案、保守孤子；亮孤子、暗孤子和灰孤子；频率梳、空间无序、时空混沌、缺陷介导湍流甚至巨浪。 所有这些非线性特征的计算机模拟与实验室实验之间存在一一对应的关系，并应用于超快光通信、光存储器、神经网络、频率标准、光钟、未来的GPS、天文学和量子技术。 这一切都是通过“对激光器、非线性光学和量子光学系统时空动力学的新见解，以及通过开发和应用小型计算的强大技术”（2011年物理学会和意大利物理学会的奥奇亚利尼奖章和奖金）得以实现的。 显示英文摘要

We all know that the first laser device was realised by Theodore Maiman at Hughes Labs in 1960. Less known is that the very first computer simulations of the relaxation oscillations displayed by Maiman's laser were also performed in 1960 on a digital IBM 704 computer. The reason is that lasers and almost all photonic devices are described by nonlinear equations that are more often than not impossible to be solved analytically, i.e. on a piece of paper. Since then the development and applications of lasers and photonic devices has progressed hand in hand with computer simulations and numerical programming. In this review we introduce and numerically solve the model equations for a variety of devices, lasers, lasers with modulated parameters, lasers with injection, Kerr resonators, saturable absorbers and optical parametric oscillators. By using computer simulations we demonstrate stability and instability of nonlinear solutions in these photonic devices via pitchfork, saddle-node, Hopf and Turing bifurcations; bistability, nonlinear oscillations, deterministic chaos, Turing patterns, conservative solitons; bright, dark and grey cavity solitons; frequency combs, spatial disorder, spatio-temporal chaos, defect mediated turbulence and even rogue waves. There has been a one-to-one correspondence between computer simulations of all these nonlinear features and laboratory experiments with applications in ultrafast optical communications, optical memories, neural networks, frequency standards, optical clocks, future GPS, astronomy and quantum technologies. All of this has been made possible by 'novel insights into spatio-temporal dynamics of lasers, nonlinear and quantum optical systems, achieved through the development and application of powerful techniques for small-scale computing' (2011 Occhialini Medal and Prize of the Institute of Physics and Societa' Italiana di Fisica).

替换提交 (展示 3 之 3 条目 )

[8] arXiv:2506.06182 (替换) [中文pdf, pdf, 其他]

标题： 可积的簇映射类型$D_{2N}$的变形 显示英文标题

标题： Integrable deformations of cluster maps of type $D_{2N}$

Wookyung Kim

评论： 拼写错误已更正

主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph) ; 组合数学 (math.CO)

在本文中，我们将与Hone和Mase共同工作的主要结果之一进行了扩展，其中我们研究了一种变形的类型$D_{4}$映射，以推广到类型$D_{2N}$的一般情况，对于$N\geq3$而言。这可以通过在与Grabowski和Hone共同工作中引入的“局部展开”操作来实现。该操作涉及将一个特定的子箭图插入到变形类型$D_{4}$映射的Laurent化所产生的箭图中。这种插入产生了一个新的箭图，通过变形类型$D_{6}$映射的Laurent化得到，从而使得对更高秩的$D_{2N}$进行系统性推广成为可能。 我们还通过热带方法研究了变形类型$D_{2N}$映射的次数增长，并猜想，对于每个$N$，该变形映射是可积的，这由代数熵检验所指示，这是检测离散动力系统可积性的标准。 显示英文摘要

In this paper, we extend one of the main results from our joint work with Hone and Mase, in which we studied a deformed type $D_{4}$ map, to the general case of the type $D_{2N}$ for $N\geq3$. This can be achieved through a ``local expansion" operation, introduced in our joint work with Grabowski and Hone. This operation involves inserting a specific subquiver into the quiver arising from the Laurentification of the deformed type $D_{4}$ map. This insertion yields a new quiver, obtained through the Laurentification of the deformed type $D_{6}$ map and thus enables systematic generalization to higher ranks $D_{2N}$. We also study the degree growth of deformed type $D_{2N}$ map via the tropical method and conjecture that, for each $N$, the deformed map is an integrable, as indicated by the algebraic entropy test, the criterion for detecting integrability in the discrete dynamical systems.

[9] arXiv:2505.12002 (替换) [中文pdf, pdf, html, 其他]

标题： 扰动长非线性平面、环状和混合表面波的演化 显示英文标题

标题： Evolution of perturbed long nonlinear plane, ring and hybrid surface waves

Benjamin Martin, Dmitri Tseluiko, Karima Khusnutdinova

评论： 38页，18图

主题： 流体动力学 (physics.flu-dyn) ; 模式形成与孤子 (nlin.PS)

二维扰动长弱非线性表面平面波、环形波和混合波的演化，由一部分环形波和两个相切平面波组成，在二维 Boussinesq-Peregrine 系统的范围内进行数值建模。 数值运行使用简化的 2+1 维 cKdV 型和 KPII 方程进行初始化和解释。 cKdV 型方程根据是否使用相关非线性一阶微分方程的一般解或奇异解（即一般解的包络），导致两种不同的模型，即 KdV$\theta$和 cKdV 方程。 KdV$\theta$方程也直接从二维 Boussinesq-Peregrine 系统中推导出来，并用于解析描述受到足够长横向有限强度扰动的线孤立子的中间二维渐近行为，而 cKdV 方程用于初始化具有局部和周期扰动的向外和向内传播的环形波。 这两个方程以及 KPII 方程都被用来模拟混合波的演化，在此我们特别展示了大局部波（ lump）可以在向内传播波的演化中作为瞬态（出现然后消失）状态出现，从而对 rogue 波的生成机制做出贡献。 对非稳态二维建模的关键特征与简化方程的相关预测进行了详细比较。 显示英文摘要

The two-dimensional evolution of perturbed long weakly-nonlinear surface plane, ring, and hybrid waves, consisting, to leading order, of a part of a ring and two tangent plane waves, is modelled numerically within the scope of the 2D Boussinesq-Peregrine system. Numerical runs are initiated and interpreted using the reduced 2+1-dimensional cKdV-type and KPII equations. The cKdV-type equation leads to two different models, the KdV$\theta$ and cKdV equations, depending on whether we use the general or singular (i.e. the envelope of the general) solution of the associated nonlinear first-order differential equation. The KdV$\theta$ equation is also derived directly from the 2D Boussinesq-Peregrine system and used to analytically describe the intermediate 2D asymptotics of line solitons subject to sufficiently long transverse perturbations of finite strength, while the cKdV equation is used to initiate outward- and inward-propagating ring waves with localised and periodic perturbations. Both of these equations, together with the KPII equation, are used to model the evolution of hybrid waves, where we show, in particular, that large localised waves (lumps) can appear as transient (emerging and then disappearing) states in the evolution of inward-propagating waves, contributing to the possible mechanisms for the generation of rogue waves. Detailed comparisons are made between the key features of the non-stationary two-dimensional modelling and relevant predictions of the reduced equations.

[10] arXiv:2510.14886 (替换) [中文pdf, pdf, html, 其他]

标题： Ruelle-Pollicott 传播子在多体系统中的非时序关联函数衰减 显示英文标题

标题： Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems

Jerónimo Duarte, Ignacio García-Mata, Diego A. Wisniacki

评论： 8页，4图。（修正了几处拼写错误）

主题： 量子物理 (quant-ph) ; 无序系统与神经网络 (cond-mat.dis-nn) ; 混沌动力学 (nlin.CD)

量子系统中信息的混乱程度由非时间顺序关联函数（OTOC）来量化，并且它是量子混沌的关键诊断工具。在具有经典对应物的一体系统中，OTOC的弛豫由Ruelle-Pollicott共振所支配。对于缺乏半经典极限的多体系统，最近的研究发现，弱开放动力学扩展的Liouvillian谱扮演了类似的角色，其中最慢的衰减率——Liouvillian间隙——编码了弛豫。在这里，我们研究了受激伊辛自旋链，并表明孤立系统中OTOC的长时间指数衰减速率等于这个内在间隙的两倍。这种对应关系甚至在可积性与混沌之间的过渡区域也持续存在，证明Liouvillian谱为理解封闭多体量子系统的弛豫和不可逆性提供了一个统一的框架。 显示英文摘要

The out-of-time-order correlator (OTOC) quantifies information scrambling in quantum systems and serves as a key diagnostic of quantum chaos. In one-body systems with a classical counterpart, the relaxation of the OTOC is governed by Ruelle-Pollicott resonances. For many-body systems lacking a semiclassical limit, recent studies have identified an analogous role played by the Liouvillian spectrum of weakly open extensions of the dynamics, where the slowest decay rate -- the Liouvillian gap -- encodes relaxation. Here we study the kicked Ising spin chain and show that the long-time exponential decay of the OTOC in the isolated system occurs at a rate equal to twice this intrinsic gap. This correspondence persists even in crossover regimes between integrability and chaos, demonstrating that the Liouvillian spectrum provides a unified framework for understanding relaxation and irreversibility in closed many-body quantum systems.