Physica D: Nonlinear Phenomena最新文献

{"title":"State–Hamiltonian Neural Networks for learning dynamical systems","authors":"Yan Wu ,&nbsp;Hong-Kun Zhang ,&nbsp;Huagui Duan","doi":"10.1016/j.physd.2025.134994","DOIUrl":"10.1016/j.physd.2025.134994","url":null,"abstract":"<div><div>Understanding the behavior of dynamical systems and their underlying physical laws has long been a central focus of research. However, previous approaches often suffer from either high data and computational demands or an inability to infer the underlying physical laws. In this paper, we propose a novel State–Hamiltonian Neural Network (State–HNN) framework that simultaneously learns a mapping from time to system state and infers the underlying Hamiltonian dynamics. Leveraging Hamiltonian mechanics, the proposed method enforces energy conservation and yields physically consistent predictions. We evaluate the method on several benchmark systems: (1) a mass–spring system; (2) a double pendulum; (3) a simple pendulum; and (4) a three-body system. In particular, we provide a detailed analysis of the three-body experiment. The results demonstrate that State–HNN accurately captures complex dynamics while preserving energy invariance, outperforming the classical Hamiltonian Neural Network (HNN) approach, particularly in high-dimensional settings.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134994"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416425","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 integrable six-wave interaction system and its space–time shifted reduction","authors":"Mark J. Ablowitz ,&nbsp;Ramesh Gupta ,&nbsp;Ziad H. Musslimani ,&nbsp;Nicholas J. Ossi","doi":"10.1016/j.physd.2025.134976","DOIUrl":"10.1016/j.physd.2025.134976","url":null,"abstract":"<div><div>The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell’s equations, a reduced system of equations governing the dynamics of the electric and polarization fields are obtained. Using a space–time multi-scale asymptotic expansion, a hierarchy of coupled equations describing the spatio-temporal evolution of the perturbed electric and polarization fields are derived. The leading order equation admits a six-wave ansatz satisfying a triad resonance condition. By removing secular terms at next order, a first order in space and time quadratically nonlinear coupled six-wave interaction system is obtained. This resulting system is tied to its integrable counterpart which was postulated by Ablowitz and Haberman in the 1970s. A reduction to a space–time shifted nonlocal three-wave system is presented. The resulting system is solved using the inverse scattering transform, which employs nonlocal symmetries between the associated eigenfunctions and scattering data; soliton solutions are then obtained. Finally, an infinite set of conservation laws for the six-wave system is derived; one is shown to be connected to its Hamiltonian structure.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134976"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362847","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":"A functional limit theorem for a dynamical system with an observable maximised on a Cantor set","authors":"Raquel Couto ,&nbsp;Ana Cristina Moreira Freitas ,&nbsp;Jorge Milhazes Freitas ,&nbsp;Mike Todd","doi":"10.1016/j.physd.2025.134989","DOIUrl":"10.1016/j.physd.2025.134989","url":null,"abstract":"<div><div>We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics, causes clustering of large observations: this is captured in the ‘decorations’ on our point processes and functional limits, an application of the theory developed in a paper by the latter three authors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134989"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416602","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":"Forced traveling waves in a population model with mobile and stationary states under a changing environment","authors":"Zhaoquan Xu ,&nbsp;Dongmei Xiao ,&nbsp;Chufen Wu","doi":"10.1016/j.physd.2025.135018","DOIUrl":"10.1016/j.physd.2025.135018","url":null,"abstract":"<div><div>We investigate the traveling wave dynamics in a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction–diffusion equation with a moving variable <span><math><mrow><mi>x</mi><mo>+</mo><mi>c</mi><mi>t</mi></mrow></math></span>, <span><math><mrow><mi>c</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed <span><math><mi>c</mi></math></span>, and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>&gt;</mo><mn>0</mn></mrow></math></span>, such that the equation model admits a forced traveling wave with speed <span><math><mi>c</mi></math></span> if and only if the environment shifting speed <span><math><mrow><mi>c</mi><mo>&gt;</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Thereby, the species cannot follow the changing environment with speed <span><math><mi>c</mi></math></span> if <span><math><mrow><mi>c</mi><mo>≤</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Compared to the well-known results on the classic Fisher’s equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. Moreover, it is proved that such a forced traveling wave is unique and globally stable if <span><math><mrow><mi>c</mi><mo>&gt;</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed <span><math><mi>c</mi></math></span> satisfies <span><math><mrow><mi>c</mi><mo>&gt;</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135018"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475980","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":"Classical-quantum simulation of single and multiple solitons generated from the KdV equation","authors":"Andrea Staino ,&nbsp;Frank Gaitan ,&nbsp;Biswajit Basu","doi":"10.1016/j.physd.2025.135012","DOIUrl":"10.1016/j.physd.2025.135012","url":null,"abstract":"<div><div>Solitons are stable, localized solitary waves that can traverse a medium keeping their shape and speed without dissipating or diffusing. The soliton is a paramount concept in nonlinear science and it has been the subject of extensive research in physics. Experiments involving solitons have been conducted in multiple domains, including nonlinear optics, plasma physics, condensed matter, fluid mechanics, information coding and transmission. Designing experiments involving solitons often relies heavily on numerical simulations for predicting system behaviour and optimizing experimental parameters. These simulations require the resolution of nonlinear partial differential equations (PDEs), which are not solvable analytically in most realistic scenarios. On the other hand, numerical resolution of nonlinear PDEs can be computationally challenging, to accurately capture soliton dynamics, interaction effects and long-term stability regimes. Hence, constructing a quantum algorithm for soliton propagation that provides a computational speedup is of great interest. A recent quantum algorithm that solves nonlinear PDEs has been established in the literature. This algorithm has been proven to offer a quadratic speedup for Navier–Stokes and Burgers’ equations. In the present paper the capability of the gradient-free quantum solver to generate soliton solutions is studied. To verify the algorithm, single- and multi-soliton solutions of the well-known Korteweg–de Vries (KdV) equation are considered. First, the reliability of the quantum solver is investigated by comparing the solitary wave obtained from the numerical integration of the KdV with the corresponding analytical solution. Subsequently, the quantum-enabled emergence of solitons from different initial profiles as well as the recovery of known collision properties of classical solitons are examined. Results of numerical simulation of the quantum algorithm are compared with exact solutions and with a classical solver and excellent agreement is found.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135012"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475982","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":"A novel three-dimensional chaotic system with spiral chaos and adjustable number of wings: application in weak underwater acoustic signal detection","authors":"Hong Yang,&nbsp;Shijia Wang,&nbsp;Guohui Li","doi":"10.1016/j.physd.2025.134965","DOIUrl":"10.1016/j.physd.2025.134965","url":null,"abstract":"<div><div>To address the shortcomings of traditional two-dimensional chaotic systems in detection performance, this paper proposes a novel three-dimensional (3D) four-wing chaotic system (3DFWCS) with spiral chaos and adjustable number of wings, and applies it to weak underwater acoustic signal detection. First, the nonlinear characteristics of 3DFWCS, such as bifurcation and Lyapunov exponent, are analyzed in detail. Second, an innovative threshold determination method based on Poincaré section mapping and fractional order refined composite multiscale fluctuation dispersion entropy is proposed. The change in the number of wings in the phase trajectory from two wings to four wings is used as the critical state for weak signal detection. Performance testing demonstrates a detection signal-to-noise ratio lower limit of -107.44 dB. Next, transient transition phenomena of the system are analyzed, revealing that the formation of four wings depends on the negative half-axis of the timing diagram of the state variable <em>z</em>. Finally, a weak signal detection method based on 3DFWCS is proposed and successfully applied to the detection of multi-spectrum periodic signals, distorted signal, ship radiated noise, and marine biological signal, verifying the effectiveness and engineering feasibility of the proposed detection method.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134965"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267936","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 sufficient frameworks for the exponential thermo-mechanical flocking in inertial spin ensembles","authors":"Seung-Yeal Ha ,&nbsp;Guanghui Jin ,&nbsp;Myeonghyeon Kim ,&nbsp;Qirui Wang","doi":"10.1016/j.physd.2025.134946","DOIUrl":"10.1016/j.physd.2025.134946","url":null,"abstract":"<div><div>We study quantitative flocking estimates for two thermo-mechanical inertial spin models. More precisely, we present a sufficient framework leading to the exponential decay of each thermo-mechanically consistent inertial spin model. For this, we derive a system of differential inequalities for relative kinetic and spin energies, when thermal and linear velocities are confined in an invariant cone, and then we explicitly obtain exponential flocking under the proposed frameworks. We also provide several numerical examples and compare them with analytical results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134946"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097239","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":"Local and global analysis of the displacement map for some near integrable systems","authors":"Francisco Braun ,&nbsp;Leonardo Pereira Costa da Cruz ,&nbsp;Joan Torregrosa","doi":"10.1016/j.physd.2025.134932","DOIUrl":"10.1016/j.physd.2025.134932","url":null,"abstract":"<div><div>In this paper, we introduce an alternative method for applying averaging theory of orders 1 and 2 in the plane. This is done by combining Taylor expansions of the displacement map with the integral form of the Poincaré–Poyntriagin–Melnikov function. It is known that, to obtain results of order 2 with averaging theory, the first-order averaging function should be identically zero. However, when working with Taylor expansions of the <span><math><mi>i</mi></math></span>th-order averaging function, we usually cannot guarantee it is identically zero. We prove that the vanishing of certain coefficients of the Taylor series of the first-order averaging function ensures it is identically zero. We present our reasoning in several concrete examples: a quadratic Lotka–Volterra system, a quadratic Hamiltonian system, the entire family of quadratic isochronous differential systems, and a cubic system. For the latter, we also show that a previous analysis contained in the literature is not correct. In none of the examples is it necessary to precisely calculate the averaging functions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134932"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097240","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":"Preface to the special issue Nonlinear processes in Fluid Dynamics","authors":"Makrina Agaoglou ,&nbsp;Jezabel Curbelo","doi":"10.1016/j.physd.2025.134966","DOIUrl":"10.1016/j.physd.2025.134966","url":null,"abstract":"<div><div>The Nonlinear Processes in Fluid Dynamics special issue covers a wide range of topics, from small-to large-scale phenomena and diverse applications, incorporating theoretical, numerical, and computational approaches. Our aim with this collection is to provide a comprehensive overview of the current state of the field, while also highlighting the most recent developments and emerging trends in nonlinear fluid dynamics research, spanning mathematical considerations to physical perspectives.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134966"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145516568","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":"Focusing fractional modified Korteweg–de Vries equation: Riemann–Hilbert method and double-pole solutions","authors":"Xiaoqian Huang,&nbsp;Huanhe Dong,&nbsp;Yong Zhang","doi":"10.1016/j.physd.2025.135006","DOIUrl":"10.1016/j.physd.2025.135006","url":null,"abstract":"<div><div>In this paper, the double-pole solutions of the focusing fractional modified Korteweg–de Vries equation are derived via the Riemann–Hilbert method. We obtain the anomalous dispersion relation from the linearized form of the equation, thereby transferring the fractional effects of the operator into the spectral domain. Then, the corresponding fractional operator function is defined, and the explicit form of the equation is expressed in terms of squared eigenfunctions. In the reflectionless case, we derive the fractional double-pole bright–bright soliton solution and double-pole breather solution. In particular, we rigorously verify the fractional double-pole bright–bright soliton and analyze its long-time asymptotic behavior. A quantitative analysis reveals that the fractional order <span><math><mi>ϵ</mi></math></span> significantly affects the velocity, peak position, and full width at half maximum of this soliton solution in the time domain. Furthermore, the amplitude and velocity of the asymptotic solutions <span><math><msubsup><mrow><mi>q</mi></mrow><mrow><mo>±</mo></mrow><mrow><mrow><mo>[</mo><mn>2</mn><mo>]</mo></mrow></mrow></msubsup></math></span> exhibit a power-law relationship, indicating that the solutions of this fractional equation display anomalous dispersion phenomena.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 135006"},"PeriodicalIF":2.9,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145416421","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}