Physica D: Nonlinear Phenomena最新文献

{"title":"Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model","authors":"D.S. Agafontsev ,&nbsp;T. Congy ,&nbsp;G.A. El ,&nbsp;S. Randoux ,&nbsp;G. Roberti ,&nbsp;P. Suret","doi":"10.1016/j.physd.2025.134956","DOIUrl":"10.1016/j.physd.2025.134956","url":null,"abstract":"<div><div>We use the spectral theory of soliton gas for the one-dimensional focusing nonlinear Schrödinger equation (fNLSE) to describe the statistically stationary and spatially homogeneous integrable turbulence emerging at large times from the evolution of the spontaneous (noise-induced) modulational instability of the elliptic “dn” fNLSE solutions. We show that a special, critically dense, soliton gas, namely the genus one bound-state soliton condensate, represents an accurate model of the asymptotic state of the “elliptic” integrable turbulence. This is done by first analytically evaluating the relevant spectral density of states which is then used for implementing the soliton condensate numerically via a random <span><math><mi>N</mi></math></span>-soliton ensemble with <span><math><mi>N</mi></math></span> large. A comparison of the statistical parameters, such as the Fourier spectrum, the probability density function of the wave intensity, and the autocorrelation function of the intensity, of the soliton condensate with the results of direct numerical fNLSE simulations with <span><math><mi>dn</mi></math></span> initial data augmented by a small statistically uniform random perturbation (a noise) shows a remarkable agreement. Additionally, we analytically compute the kurtosis of the elliptic integrable turbulence, which enables one to estimate the deviation from Gaussianity. The analytical predictions of the kurtosis values, including the frequency of its temporal oscillations at the intermediate stage of the modulational instability development, are also shown to be in excellent agreement with numerical simulations for the entire range of the elliptic parameter <span><math><mi>m</mi></math></span> of the initial <span><math><mi>dn</mi></math></span> potential.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134956"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221171","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}

{"title":"On blowup solution in NLS equation under dispersion or nonlinearity management","authors":"Jing Li ,&nbsp;Ying He ,&nbsp;Cui Ning ,&nbsp;Xiaofei Zhao","doi":"10.1016/j.physd.2025.134957","DOIUrl":"10.1016/j.physd.2025.134957","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study the dispersion-managed nonlinear Schrödinger (DM-NLS) equation &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and the nonlinearity-managed NLS (NM-NLS) equation: &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a periodic function which is equal to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and is equal to 1 when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The two models share the feature that the focusing and defocusing effects convert periodically. For the classical focusing NLS, it is known that the initial data &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mr","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134957"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221165","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}

{"title":"RTC-fPINNs: Respecting temporal causality fPINNs method for time fractional fourth order partial differential equations","authors":"Zhenqi Qi ,&nbsp;Jieyu Shi ,&nbsp;Xiaozhong Yang","doi":"10.1016/j.physd.2025.134962","DOIUrl":"10.1016/j.physd.2025.134962","url":null,"abstract":"<div><div>The accuracy of conventional fractional physics-informed neural networks (fPINNs) approach suffers dramatically for time fractional partial differential equations (PDEs) with high order derivative and strong nonlinearity. In this paper, a new respecting temporal causality fPINNs (RTC-fPINNs) method for solving time fractional fourth order PDEs is studied. To start with, an auxiliary function is introduced to transform the objective equations into two second order physical systems. Next, the Caputo fractional derivative is approximated through the L1 scheme on graded mesh for resolving the solution’s initial singularity, and correspondingly, the integer order derivatives are obtained via leveraging automatic differentiation of neural networks. Then, the reformulation loss functions corresponding to soft and hard constraints of boundary conditions are adopted to respect the intrinsic causal structure of the physical systems when training the neural network models. Finally, various numerical scenarios, including time fractional fourth order subdiffusion equation, time fractional Kuramoto–Sivashinsky and Cahn–Hilliard equations, are conducted to validate the remarkable effectiveness and robustness of the RTC-fPINNs method. It is noteworthy that, when using the same parameter values, the error accuracy of the established RTC-fPINNs approach is significantly better than that of the conventional fPINNs method.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134962"},"PeriodicalIF":2.9,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221166","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}

{"title":"Anti-aligning interaction induces gyratory flocking of simple self-propelled particles: The impact of translational noise","authors":"Daniel Escaff","doi":"10.1016/j.physd.2025.134960","DOIUrl":"10.1016/j.physd.2025.134960","url":null,"abstract":"<div><div>This report considers a set of simple active particles (non-self-rotating particles) interacting due to a purely anti-aligning force. Recently, it has been shown that such anti-aligning interaction may induce a finite wavelength instability. The instability occurs with an oscillatory frequency. Consequently, the system displays pattern formation. The formed patterns consist of propagative dissipative structures (two counterpropagating traveling waves). Here, we explore the impact of including translational noise in the dynamics. The finite wavelength instability persists; however, the oscillatory frequency only persists if the particle’s self-propulsion speed is larger enough than the translational noise intensity. We focus on this case. Near criticality, where fluctuations predominate, it is possible to distinguish propagative patterns. Moving away from criticality, a new pattern emerges via a secondary transition. Namely, a hexagonal structure formed of rotating clusters. These clusters rotate in unison, giving rise to a global gyratory synchrony. This secondary transition is discontinuous. Finally, we discuss the main ingredients that induce this sort of rotatory synchronization, showing that short-range repulsion might produce a similar effect to translational noise.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134960"},"PeriodicalIF":2.9,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221168","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}

{"title":"Hamiltonian Monte Carlo with asymmetrical momentum distributions","authors":"Soumyadip Ghosh,&nbsp;Yingdong Lu,&nbsp;Tomasz Nowicki","doi":"10.1016/j.physd.2025.134952","DOIUrl":"10.1016/j.physd.2025.134952","url":null,"abstract":"<div><div>Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new dynamical and probabilistic arguments. The convergence is rigorously established under significantly weaker conditions, which among others allow for general auxiliary distributions. In our framework, we show that plain HMC with asymmetrical momentum distributions breaks a key self-adjointness requirement. We propose a modified version of HMC, that we call the Alternating Direction HMC (AD-HMC), which overcomes this difficulty. Sufficient conditions are established under which AD-HMC exhibits geometric convergence in Wasserstein distance. The geometric convergence analysis is extended to when the Hamiltonian motion is approximated by the leapfrog symplectic integrator, where an additional Metropolis–Hastings rejection step is required. Numerical experiments suggest that AD-HMC can generalize a popular dynamic auxiliary scheme to show improved performance over HMC with Gaussian auxiliaries.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134952"},"PeriodicalIF":2.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221170","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}

{"title":"Reconstructing turbulence: A deep learning–enhanced interpolation approach","authors":"Filippos Sofos ,&nbsp;Dimitris Drikakis ,&nbsp;Ioannis William Kokkinakis","doi":"10.1016/j.physd.2025.134958","DOIUrl":"10.1016/j.physd.2025.134958","url":null,"abstract":"<div><div>High-resolution data are essential for analysing turbulent flows, yet direct numerical simulations are often computationally prohibitive. Super-resolution based on deep learning (DL) offers a promising alternative for reconstructing high-fidelity fields from coarse data. This study introduces and validates a novel hybrid framework that combines classical interpolation with a convolutional neural network (CNN) to perform super-resolution on two-dimensional turbulent flow fields. The architecture is designed to be computationally efficient and physically consistent, leveraging interpolation as a method to assist in simplifying the reconstruction task for the DL model. We evaluated the framework on three distinct turbulent flow cases—interior room airflow, sudden expansion corner flow, and turbulent channel flow—using data from implicit Large Eddy Simulations. The performance was benchmarked against both standalone interpolation methods and conventional CNN-only architectures. Results demonstrate that the hybrid approach provides superior reconstruction accuracy, as quantified by numerical measures including peak signal-to-noise ratio and the structural similarity index. Furthermore, we validate the physical consistency of the reconstructed fields by analysing their energy spectra and turbulence probability density functions, confirming that the model faithfully reproduces the essential characteristics of turbulent flow physics. This work presents a practical and effective tool for generating high-quality turbulence data at a fraction of the computational cost required by traditional methods.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134958"},"PeriodicalIF":2.9,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221169","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}

{"title":"Learning symmetries and non-Euclidean data representations via collective dynamics of generalized Kuramoto oscillators","authors":"Vladimir Jaćimović ,&nbsp;Ron Hommelsheim","doi":"10.1016/j.physd.2025.134953","DOIUrl":"10.1016/j.physd.2025.134953","url":null,"abstract":"<div><div>Learning low-dimensional representations of data is the central problem of modern machine learning (ML). Recently, it has been widely recognized that some ubiquitous data sets are more faithfully represented in curved manifolds, rather than in Euclidean spaces. This observation motivated extensive experiments with non-Euclidean deep learning architectures. In many setups, data embeddings on spheres, hyperbolic spaces or matrix manifolds enable more compact models and efficient algorithms. In the present paper we argue that Kuramoto models (including their higher-dimensional generalizations) provide a powerful framework for inferring intrinsic curvature and hidden symmetries of the data. Kuramoto ensembles naturally encode actions of transformation groups (such as special orthogonal, unitary and Lorentz groups). Following decades of studies of the Kuramoto model and its extensions, the corresponding group-theoretic framework is well established. This provides a solid theoretical foundation for geometry-informed architectures. We overview families of probability distributions on spheres and hyperbolic balls which are associated with various Kuramoto models. These probability distributions provide statistical models for encoding uncertainties and designing inference algorithms in geometric deep learning. Due to their favorable properties, Kuramoto networks can be trained via standard backpropagation method.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134953"},"PeriodicalIF":2.9,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159067","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}

{"title":"Particle, kinetic and hydrodynamic models for sea ice floes, Part I: Non-rotating floes","authors":"Quanling Deng ,&nbsp;Seung-Yeal Ha","doi":"10.1016/j.physd.2025.134951","DOIUrl":"10.1016/j.physd.2025.134951","url":null,"abstract":"<div><div>We introduce a comprehensive modeling framework for the dynamics of sea ice floes using particle, kinetic, and hydrodynamic approaches. Building upon the foundational work of Ha and Tadmor on the Cucker–Smale model for flocking, we derive a Vlasov-type kinetic formulation and a corresponding hydrodynamic description. The particle model incorporates essential physical properties of sea ice floes, including size, position, velocity, and interactions governed by Newtonian mechanics. By extending these principles, the kinetic model captures large-scale features through the phase-space distribution, and we also present a hydrodynamic model using the velocity moments and a suitable closure condition. In this paper, as an idea-introductory step, we assume that ice floes are non-rotating and focus on the linear velocity dynamics. Our approach highlights the role of contact forces, ocean drag effects, and conservation laws in the multiscale description of sea ice dynamics, offering a potential pathway for the improved understanding and prediction of sea ice behaviors in changing climatic conditions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134951"},"PeriodicalIF":2.9,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159066","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}

{"title":"Unraveling multiple 1:1 entrainment regions in the Arnold onion diagram: A study of the circadian Novak–Tyson model","authors":"Emel Khan ,&nbsp;Lawan Wijayasooriya ,&nbsp;Pejman Sanaei","doi":"10.1016/j.physd.2025.134949","DOIUrl":"10.1016/j.physd.2025.134949","url":null,"abstract":"<div><div>The entrainment of biological oscillators is a fundamental problem in studying dynamical systems and synchronization. The Arnold onion diagram is a key tool for visualizing entrainment patterns in a two-dimensional parameter space, defined by period (<span><math><mi>T</mi></math></span>) and photoperiod (<span><math><mi>χ</mi></math></span>). This paper investigates the entrainment behavior of various oscillatory regimes in the Novak–Tyson (NT) model. While previous studies have documented the presence of Arnold onions featuring a single 1:1 entrainment region, our work introduces the novel emergence of multiple disconnected 1:1 entrainment regions within these diagrams. Through the analysis of dynamical systems, we show that multiple Arnold onions emerge for an unforced system near the Hopf bifurcation, which behaves as a damped oscillator. These findings offer new insights into the complex mechanisms underlying circadian seasonality and its dependence on intrinsic oscillator dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134949"},"PeriodicalIF":2.9,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145221167","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}

{"title":"On the combined method for solving the inverse problem of the Zakharov–Shabat system","authors":"S.B. Medvedev ,&nbsp;I.A. Vaseva ,&nbsp;M.P. Fedoruk","doi":"10.1016/j.physd.2025.134942","DOIUrl":"10.1016/j.physd.2025.134942","url":null,"abstract":"<div><div>We study the combined method for solving the inverse problem of the Zakharov–Shabat system associated with the nonlinear Schrödinger equation. The method is based on a high-precision algorithm for the Gelfand–Levitan–Marchenko equation for a continuous spectrum and the Darboux method for a discrete spectrum. A comparison of the combined Darboux method and the GLME-based algorithm is made.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134942"},"PeriodicalIF":2.9,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159060","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}