Physica D: Nonlinear Phenomena最新文献_第6页

Exponential asymptotics of dark and bright solitons in the discrete nonlinear Schrödinger equation 离散非线性Schrödinger方程中暗孤子和亮孤子的指数渐近性

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-08 DOI: 10.1016/j.physd.2025.134848

F.T. Adriano , A.N. Hasmi , R. Kusdiantara , H. Susanto

{"title":"Exponential asymptotics of dark and bright solitons in the discrete nonlinear Schrödinger equation","authors":"F.T. Adriano , A.N. Hasmi , R. Kusdiantara , H. Susanto","doi":"10.1016/j.physd.2025.134848","DOIUrl":"10.1016/j.physd.2025.134848","url":null,"abstract":"<div><div>We investigate the existence and linear stability of solitons in the nonlinear Schrödinger lattices in the strong coupling regime. Focusing and defocusing nonlinearities are considered, giving rise to bright and dark solitons. In this regime, the effects of lattice discreteness become exponentially small, requiring a beyond-all-orders analysis. To this end, we employ exponential asymptotics to derive soliton solutions and examine their stability systematically. We show that only two symmetry-related soliton configurations are permissible: onsite solitons centered at lattice sites and intersite solitons positioned between adjacent sites. Although the instability of intersite solitons due to real eigenvalue pairs is known numerically, a rigorous analytical account, <em>particularly for dark solitons</em>, has been lacking. Our work fills this gap, yielding analytical predictions that match numerical computations with high accuracy. We also establish the linear stability of onsite bright solitons. While the method cannot directly resolve the quartet eigenvalue-induced instability of onsite dark solitons due to the continuous spectrum covering the entire imaginary axis, we conjecture an eigenvalue-counting argument that supports their instability. Overall, our application of the exponential asymptotics method shows the versatility of this approach for addressing multiscale problems in discrete nonlinear systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134848"},"PeriodicalIF":2.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809601","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

Elastic interaction of counter-propagating waves of arbitrary amplitude on the surface of a magnetic fluid in a tangential magnetic field in 3D geometry 三维几何中切向磁场中磁流体表面上任意振幅的反传播波的弹性相互作用

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-08 DOI: 10.1016/j.physd.2025.134885

Nikolay M. Zubarev , Olga V. Zubareva

引用次数: 0

Cut-offs in a degenerate advection–reaction–diffusion equation — a case study 简并平流-反应-扩散方程的截止点-一个案例研究

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-07 DOI: 10.1016/j.physd.2025.134870

Nikola Popović , Mariya Ptashnyk , Zak Sattar

{"title":"Cut-offs in a degenerate advection–reaction–diffusion equation — a case study","authors":"Nikola Popović , Mariya Ptashnyk , Zak Sattar","doi":"10.1016/j.physd.2025.134870","DOIUrl":"10.1016/j.physd.2025.134870","url":null,"abstract":"<div><div>We investigate the effect of a Heaviside cut-off on the front propagation dynamics of a degenerate advection–reaction–diffusion equation. In particular, we consider two formulations of the equation, one with the cut-off function multiplying the reaction kinetics alone and one in which the cut-off is also applied to the advection term. We prove the existence and uniqueness of a “critical” front solution in both cases, and we derive the leading-order correction to the front propagation speed in dependence on the advection strength and the cut-off parameter. We show that, while the asymptotics of the correction in the cut-off parameter remains unchanged to leading order when the advection term is cut off, the corresponding coefficient is different. Finally, we consider a generalised family of advection–reaction–diffusion equations, and we identify scenarios in which the application of a cut-off to the advection term substantially affects the front propagation speed. Our analysis relies on geometric techniques from dynamical systems theory and, specifically, on geometric desingularisation, also known as “blow-up”.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134870"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864477","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

Slushball Earth equilibria in a one-dimensional energy balance model 一维能量平衡模型中的泥球地球平衡

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-07 DOI: 10.1016/j.physd.2025.134866

Aksel Samuelsberg, Per Kristen Jakobsen

{"title":"Slushball Earth equilibria in a one-dimensional energy balance model","authors":"Aksel Samuelsberg, Per Kristen Jakobsen","doi":"10.1016/j.physd.2025.134866","DOIUrl":"10.1016/j.physd.2025.134866","url":null,"abstract":"<div><div>Understanding the widespread glaciations of the late Neoproterozoic era (715–635 Ma) is important for understanding the evolution of life on Earth. A Waterbelt state has been proposed as a more biologically friendly alternative to the Snowball Earth hypothesis. It was subsequently shown that an open tropical ocean can be sustained by a so-called “Jormungand mechanism”, where darker, bare sea ice at the descending edge of the Hadley cell halts the runaway ice-albedo feedback synonymous with Snowball Earth. However, the geological evidence for thick, active glaciers at sea level in the deep tropics during these glaciations presents a problem for the Waterbelt hypothesis that has received limited attention in the literature. We study a diffusive, one-dimensional energy balance model (EBM) with a Jormungand mechanism, where also the effects at the ascending edge of the Hadley cell are included. The EBM is solved using an analytical approach, the boundary integral method. The modified Jormungand mechanism produces several unstable Slushball Earth states in the EBM, in addition to the Waterbelt states. These Slushball Earth states are similar to Snowball Earth, but with a series of water belts over lower latitudes. Implications for the Neoproterozoic glaciations are discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134866"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887063","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

The complexity dynamics of grokking grokking的复杂性动力学

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-07 DOI: 10.1016/j.physd.2025.134859

Branton DeMoss, Silvia Sapora, Jakob Foerster, Nick Hawes, Ingmar Posner

{"title":"The complexity dynamics of grokking","authors":"Branton DeMoss, Silvia Sapora, Jakob Foerster, Nick Hawes, Ingmar Posner","doi":"10.1016/j.physd.2025.134859","DOIUrl":"10.1016/j.physd.2025.134859","url":null,"abstract":"<div><div>We demonstrate the existence of a complexity phase transition in neural networks by studying the grokking phenomenon, where networks suddenly transition from memorization to generalization long after overfitting their training data. To characterize this phase transition, we introduce a theoretical framework for measuring complexity based on rate–distortion theory and Kolmogorov complexity, which can be understood as principled lossy compression for networks. We find that properly regularized networks exhibit a sharp phase transition: complexity rises during memorization, then falls as the network discovers a simpler underlying pattern that generalizes. In contrast, unregularized networks remain trapped in a high-complexity memorization phase. We establish an explicit connection between our complexity measure and generalization bounds, providing a theoretical foundation for the link between lossy compression and generalization. Our framework achieves compression ratios 30-40<span><math><mo>×</mo></math></span> better than naïve approaches, enabling precise tracking of complexity dynamics. Finally, we introduce a regularization method based on spectral entropy that encourages networks toward low-complexity representations by penalizing their intrinsic dimension.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134859"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858481","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

Physics-informed spectral approximation of Koopman operators Koopman算子的物理信息谱近似

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-06 DOI: 10.1016/j.physd.2025.134835

Dimitrios Giannakis , Claire Valva

{"title":"Physics-informed spectral approximation of Koopman operators","authors":"Dimitrios Giannakis , Claire Valva","doi":"10.1016/j.physd.2025.134835","DOIUrl":"10.1016/j.physd.2025.134835","url":null,"abstract":"<div><div>Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for supervised and unsupervised learning of nonlinear dynamical systems, and has received considerable interest in recent years. Here, we propose a data-driven technique for spectral approximation of Koopman operators of continuous-time, measure-preserving ergodic systems that is asymptotically consistent and makes direct use of known equations of motion (physics). Our approach is based on a bounded transformation of the Koopman generator (an operator implementing directional derivatives of observables along the dynamical flow), followed by smoothing by a Markov semigroup of kernel integral operators. This results in a skew-adjoint, compact operator whose eigendecomposition is expressible as a variational generalized eigenvalue problem. We develop Galerkin methods to solve this eigenvalue problem and study their asymptotic consistency in the large-data limit. A key aspect of these methods is that they are physics-informed, in the sense of making direct use of dynamical vector field information through automatic differentiation of kernel functions. Solutions of the eigenvalue problem reconstruct evolution operators that preserve unitarity of the underlying Koopman group while spectrally converging to it in a suitable limit. In addition, the computed eigenfunctions have representatives in a reproducing kernel Hilbert space, enabling out-of-sample evaluation of learned dynamical features. Numerical experiments performed with this method on integrable and chaotic low-dimensional systems demonstrate its efficacy in extracting dynamically coherent observables under complex dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134835"},"PeriodicalIF":2.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887062","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

Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems 连续波中的自发对称性破缺，线性耦合双峰系统中的暗孤子和涡旋

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-05 DOI: 10.1016/j.physd.2025.134854

Hidetsugu Sakaguchi , Boris A. Malomed

{"title":"Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems","authors":"Hidetsugu Sakaguchi , Boris A. Malomed","doi":"10.1016/j.physd.2025.134854","DOIUrl":"10.1016/j.physd.2025.134854","url":null,"abstract":"<div><div>We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength <span><math><mrow><mi>g</mi><mo>=</mo><mn>2</mn></mrow></math></span> of the nonlinear repulsion between the components, and linear coupling between them. A more general system of coupled Gross–Pitaevskii (GP) equations, with <span><math><mrow><mi>g</mi><mo>≠</mo><mn>2</mn></mrow></math></span> and the linear mixing between the components, is considered too. The latter system is introduced in its one- and two-dimensional (1D and 2D) forms. A new finding is the spontaneous symmetry breaking (SSB) of bimodal CW (continuous-wave) states in the case of <span><math><mrow><mi>g</mi><mo>></mo><mn>1</mn></mrow></math></span> (in the absence of the linear coupling, it corresponds to the immiscibility of the nonlinearly interacting components). The SSB is represented by an exact asymmetric CW solution. An exact solution is also found, in the case of <span><math><mrow><mi>g</mi><mo>=</mo><mn>3</mn></mrow></math></span>, for stable dark solitons (DSs) supported by the asymmetric CW background. For <span><math><mrow><mi>g</mi><mo>≠</mo><mn>3</mn></mrow></math></span>, numerical solutions are produced for stable DSs supported by the same background. Moreover, we identify a parameter domain where the fully miscible (symmetric) CW background maintains stable DSs with the <em>inner SSB</em> (separation between the components) in its core. In 2D, the GP system produces stable vortex states with a shift between the components and broken isotropy. The vortices include ones with the inter-component shift imposed by the asymmetric CW background, and states supported by the symmetric background, in which the intrinsic shift (splitting) is exhibited by vortical cores of the two components.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134854"},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779737","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

Phase boundary dynamics for ice nucleation and growth processes in fresh and sea water 淡水和海水中冰成核和生长过程的相边界动力学

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-05 DOI: 10.1016/j.physd.2025.134855

Bernd Kutschan , Silke Thoms , Andrea Thom , Raghav Pathak , Tim Ricken

引用次数: 0

Machine learning-based estimation of correlation dimension from short chaotic time series 基于机器学习的短混沌时间序列相关维数估计

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-05 DOI: 10.1016/j.physd.2025.134869

Shuang Zhou , Shiyu Wang , Herbert Ho-Ching Iu , Yingqian Zhang , Hao Zhang

{"title":"Machine learning-based estimation of correlation dimension from short chaotic time series","authors":"Shuang Zhou , Shiyu Wang , Herbert Ho-Ching Iu , Yingqian Zhang , Hao Zhang","doi":"10.1016/j.physd.2025.134869","DOIUrl":"10.1016/j.physd.2025.134869","url":null,"abstract":"<div><div>Fractal dimension is an important tool for describing complex systems, while correlation dimension is a type of fractal dimension of time series. It can give a more accurate understanding of the characteristics of the system and plays an important role in practical applications. To address the challenge of accurately calculating the correlation dimension of short chaotic data, this paper explores a machine learning-based approach. This method leverages the universal approximation theory of neural networks to compare the Long Short-Term Memory (LSTM) network, the Transformer architecture, and the Backpropagation (BP) network in deep learning, and then selects the optimal approach. Ultimately, the method integrates the backpropagation (BP) neural network with a genetic programming (GP) algorithm for the calculation of the correlation dimension, thereby constructing a novel model. This method aims to expand the volume of chaotic short data and thereby better utilize data information. Initially, a BP neural network with ten hidden layer neurons is constructed, combined with the calculation of correlation dimension to form a new method. Subsequently, simulations are conducted on various commonly encountered chaotic systems, including Lorenz, Hénon, Chen, Logistic systems, solar activity time series and daily female births time series. And their mean squared error (MSE) values are recorded after data augmentation. Finally, the correlation dimensions of these expanded data sets are recalculated and compared with their original values. The findings reveal a remarkable proximity to the theoretical values, thereby validating the method's efficacy in augmenting chaotic short-term sequences. This approach not only enhances the utilization of original chaotic time series data but also paves the way for extracting deeper insights and greater value from short chaotic data.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134869"},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907028","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

N-breather solutions of the Camassa–Holm equation on oscillatory backgrounds 振荡背景下Camassa-Holm方程的n呼吸解

IF 2.9 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-08-05 DOI: 10.1016/j.physd.2025.134847

Ruomeng Li , Xianguo Geng , Abdul-Majid Wazwaz , Manxue Liu

引用次数: 0