Physica D: Nonlinear Phenomena最新文献

{"title":"The Jacobian conjecture and integrability of associated partial differential equations","authors":"Yisong Yang","doi":"10.1016/j.physd.2025.134862","DOIUrl":"10.1016/j.physd.2025.134862","url":null,"abstract":"<div><div>The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work obtains broad families of polynomial maps satisfying the conjecture in all dimensions and of arbitrarily high degrees. Furthermore, it is shown that a reformulated multiply parametrized version of the conjecture in all dimensions enables a separation of the Jacobian equation into a system of subequations which may be integrated systematically rendering a settlement of the parametrized Jacobian problem in this context.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134862"},"PeriodicalIF":2.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890841","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 modified Korteweg–de Vries equation soliton gas on a nonzero background","authors":"Xiaoen Zhang ,&nbsp;Liming Ling","doi":"10.1016/j.physd.2025.134890","DOIUrl":"10.1016/j.physd.2025.134890","url":null,"abstract":"<div><div>In this paper, we consider a soliton gas of the focusing modified Korteweg–de Vries generated from the <span><math><mi>N</mi></math></span>-soliton solutions on a nonzero background. The spectral soliton density is chosen on the pure imaginary axis, excluding the branch cut <span><math><mrow><msub><mrow><mi>Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mfenced><mrow><mo>−</mo><mi>i</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mrow></math></span>. In the limit <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, we establish the Riemann–Hilbert Problem of the soliton gas. Using the Deift-Zhou nonlinear steepest-descent method, this soliton gas on a nonzero background will decay to a constant background as <span><math><mrow><mi>x</mi><mo>→</mo><mo>+</mo><mi>∞</mi></mrow></math></span>, while its asymptotics as <span><math><mrow><mi>x</mi><mo>→</mo><mo>−</mo><mi>∞</mi></mrow></math></span> can be expressed with a Riemann Theta function, attached to a Riemann surface with genus-two. We also analyze the large <span><math><mi>t</mi></math></span> asymptotics over the entire spatial domain, which is divided into three distinct asymptotic regions depending on the ratio <span><math><mrow><mi>ξ</mi><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></mfrac></mrow></math></span>. Using the similar method, we provide the leading-order asymptotic behaviors for these three regions and exhibit the dynamics of large <span><math><mi>t</mi></math></span> asymptotics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134890"},"PeriodicalIF":2.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879376","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":"Classification and stability of periodic solutions of a relativistic MEMS","authors":"Sunwei Dai,&nbsp;Weihan Li,&nbsp;Xingchen Yu","doi":"10.1016/j.physd.2025.134884","DOIUrl":"10.1016/j.physd.2025.134884","url":null,"abstract":"<div><div>We establish a complete classification of positive periodic solutions for a relativistic micro-electro-mechanical system (MEMS), revealing two distinct solution families with qualitatively different asymptotic behaviors under large electrode separation. Moreover, we present a necessary and sufficient condition for the existence of both asymptotically stable and unstable periodic solutions when the driving voltage’s angular frequency is sufficiently enough.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134884"},"PeriodicalIF":2.9,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864476","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":"Hydromagnetic oscillatory instability in non-linear thermohaline convection of chemically reactive Casson fluid through a porous layer: Effect of open boundary","authors":"Raju Sen ,&nbsp;Shaowei Wang ,&nbsp;Rishi Raj Kairi","doi":"10.1016/j.physd.2025.134883","DOIUrl":"10.1016/j.physd.2025.134883","url":null,"abstract":"<div><div>This work investigates oscillatory instability in non-linear thermohaline convection of Casson fluid flow through a porous medium open at the top. The problem uses a non-linear Oberbeck–Boussinesq approximation to describe how fluid density changes. It also includes heating due to viscous dissipation under an externally imposed vertical magnetic field, accompanied by a first-order chemical reaction. The flow field is non-dimensionalized with the help of the proper choice of scales, while the base flow is then perturbed with a small fluctuation to examine instability theory. The Runge–Kutta method, combined with the shooting technique, is employed for the numerical integration of eigenvalue problems that arise from stability analyses. The graphical illustration is made for critical thermal Rayleigh numbers concerning each flow-governing parameter, and quantitative values in tabular form are provided. Our results reveal that the non-linear solutal effect <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> acts to stabilize the solute distribution over the two boundaries when the lower boundary has a higher concentration of solute than the upper boundary (<span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>&lt;</mo><mn>0</mn></mrow></math></span>). Under zero solute transport conditions (<span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>), however, <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> is linear. Of note is the fact that the stabilized <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> has become destabilized because of the large amount of solute at the upper boundary relative to that at the lower (<span><math><mrow><mi>R</mi><msub><mrow><mi>a</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math></span>). Still, in every case, the non-linear thermal effect <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> acts to destabilize. Also, the Hartmann number <span><math><mrow><mi>H</mi><mi>a</mi></mrow></math></span> delays the onset of convection and reduces the region of subcritical instabilities. At negative solutal Rayleigh numbers, the obliqueness of the basic flow stabilizes the thermal instability, while transverse rolls correspond to the most unstable mode for the onset of convection. A lower Casson parameter (<span><math><mi>β</mi></math></span>) causes the fluid to exhibit very extreme non-Newtonian behavior, which prevents oscillatory activity. Higher chemical reactivity shifts streamlines upward, directs isotherms towards the open boundary, and centralizes isohalines. Strong reactivity also weakens the transverse rolls and causes symmetrical isotherm vortices near the boundaries, whereas the isohalines begin by rising and then spreading through ","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134883"},"PeriodicalIF":2.9,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860938","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":"Verification, enumeration and generation of multistate canalizing functions","authors":"Xue Jia,&nbsp;Haitao Li","doi":"10.1016/j.physd.2025.134879","DOIUrl":"10.1016/j.physd.2025.134879","url":null,"abstract":"<div><div>This paper explores the characteristics of canalizing functions with multiple states by using the semi-tensor product of matrices. A criterion is derived from the matrix expression to verify whether a logical function is canalizing. Then, a method is presented to calculate the number of multistate canalizing functions (MSCFs). Finally, two algorithms are provided for generating MSCFs and semi-nested MSCFs.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134879"},"PeriodicalIF":2.9,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858485","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":"Synchronization–intermittent synchronization transition and the uniqueness of absolutely continuous invariant measure in coupled tent map lattice","authors":"Yiqian Wang,&nbsp;Junke Zhang","doi":"10.1016/j.physd.2025.134874","DOIUrl":"10.1016/j.physd.2025.134874","url":null,"abstract":"<div><div>We develop a new geometric-combinatorial method to study synchronization, intermittent synchronization, and the absolutely continuous invariant measure of a two-node coupled map lattice (CML) for a class of tent maps whose slope <span><math><mrow><mi>k</mi><mo>≤</mo><mn>2</mn></mrow></math></span>. We prove that with a coupling <span><math><mrow><mi>c</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow><mo>∪</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span>, where <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>k</mi></mrow></mfrac><mo>)</mo></mrow></mrow></math></span>, there exists a unique absolutely continuous invariant measure and intermittent synchronization occurs, that is, almost every point enters and exits an arbitrarily small neighborhood of the diagonal infinitely many times. In contrast, for <span><math><mrow><mi>c</mi><mo>∈</mo><mrow><mo>(</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>,</mo><mn>1</mn><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span>, synchronization occurs for every point. This shows that <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> is the transition point of the coupling strength.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134874"},"PeriodicalIF":2.9,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858484","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":"Solid-state dewetting of axisymmetric thin film on axisymmetric curved-surface substrates: Modeling and simulation","authors":"Zhenghua Duan,&nbsp;Meng Li,&nbsp;Chunjie Zhou","doi":"10.1016/j.physd.2025.134871","DOIUrl":"10.1016/j.physd.2025.134871","url":null,"abstract":"<div><div>In this work, we consider the solid-state dewetting of an axisymmetric thin film on a curved-surface substrate, with the assumption that the substrate morphology is also axisymmetric. Under the assumptions of axisymmetry, the surface evolution problem on a curved-surface substrate can be reduced to a curve evolution problem on a static curved substrate. Based on the thermodynamic variation of the anisotropic surface energy, we thoroughly derive a sharp-interface model that is governed by anisotropic surface diffusion, along with appropriate boundary conditions. The continuum system satisfies the laws of energy decay and volume conservation, which motivates the design of a structure-preserving numerical algorithm for simulating the mathematical model. We introduce an arclength parameterization of the generated curve on the axisymmetric curved substrate surface, which plays a crucial role in the subsequent construction of the structure-preserving approximation. By introducing a symmetrized surface energy matrix, we derive a novel symmetrized variational formulation. Then, by carefully discretizing the boundary terms of the variational formulation, we establish an unconditionally energy-stable parametric finite element approximation of the axisymmetric system. By applying an ingenious correction method, we further develop another structure-preserving method that can preserve both the energy stability and volume conservation properties. Finally, we present extensive numerical examples to demonstrate the convergence and structure-preserving properties of our proposed numerical scheme. Additionally, several interesting phenomena are explored, including the migration of ‘small’ particles on a curved-surface substrate generated by curves with positive or negative curvature, pinch-off events, and edge retraction.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134871"},"PeriodicalIF":2.9,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830995","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":"End-to-end Artificial Intelligence to analyze dynamical processes: A linear benchmark test","authors":"Emanuele Salgarollo,&nbsp;João Valle,&nbsp;Matteo Sangiorgio,&nbsp;Fabio Dercole","doi":"10.1016/j.physd.2025.134880","DOIUrl":"10.1016/j.physd.2025.134880","url":null,"abstract":"<div><div>We envisage AI architectures to analyze complex time series in an end-to-end fashion, meaning that the quantitative metrics of the time series are learned directly from data, without the use of specific human-thought algorithms. That is, we challenge AI to learn those specific algorithms. We present a first step in this direction, a benchmark test on linear dynamical processes. We tackle the archetypical task of learning the eigenvalues of the state-transition matrix of a linear (discrete-time, stable) dynamical system, from output data. We train a scalable LSTM neural network with artificially generated data from random matrices of dimension 2-to-5. With noise-free data, the performance of the trained network is very good (average <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>955</mn></mrow></math></span>), especially in estimating the dominant eigenvalues, whereas there is space for improvements on non-dominant real eigenvalues and on the dimension of the generating matrix. Remarkably, the performance is robust to measurement noise and the network outperforms the mean-square identification of the corresponding AR process (the latter giving exact eigenvalues on noise-free data) at noise standard deviation starting from <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134880"},"PeriodicalIF":2.9,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858482","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":"Data-driven system identification using quadratic embeddings of nonlinear dynamics","authors":"Stefan Klus ,&nbsp;Joel-Pascal Ntwali N’konzi","doi":"10.1016/j.physd.2025.134839","DOIUrl":"10.1016/j.physd.2025.134839","url":null,"abstract":"<div><div>We propose a novel data-driven method called QENDy (<em>Quadratic Embedding of Nonlinear Dynamics</em>) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations. The approach is based on an embedding of the system into a higher-dimensional feature space in which the dynamics become quadratic. Just like SINDy (<em>Sparse Identification of Nonlinear Dynamics</em>), our method requires trajectory data, time derivatives for the training data points, which can also be estimated using finite difference approximations, and a set of preselected basis functions, called <em>dictionary</em>. We illustrate the efficacy and accuracy of QENDy with the aid of various benchmark problems and compare its performance with SINDy and a deep learning method for identifying quadratic embeddings. Furthermore, we analyze the convergence of QENDy and SINDy in the infinite data limit, highlight their similarities and main differences, and compare the quadratic embedding with linearization techniques based on the Koopman operator.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134839"},"PeriodicalIF":2.9,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858483","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 turbulence spectrum for compressive modes in astrophysical applications","authors":"Elena Popova,&nbsp;Alexander Philippov,&nbsp;Roald Sagdeev","doi":"10.1016/j.physd.2025.134845","DOIUrl":"10.1016/j.physd.2025.134845","url":null,"abstract":"<div><div>Accretion flows onto supermassive black holes are magnetized and vigorously turbulent. Magnetically arrested disks are the leading scenarios for accretion onto black holes in our galaxy, Sgr A* and M87. Despite its significance, the properties of turbulence in these flows remain largely unexplored. In this paper we present initial analysis of turbulence spectra in an extremely high-resolution H-AMR simulation data (effective resolution of 5376 <span><math><mo>×</mo></math></span> 2304 <span><math><mo>×</mo></math></span> 230 cells) used to solve the general relativistic magnetohydrodynamics (GRMHD) equations for a spinning black hole in Kerr–Schild coordinates. We identify an inertial interval with a spectral index <span><math><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math></span> in the turbulent disk for the plasma kinetic energy in the accretion disk near the event horizon.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134845"},"PeriodicalIF":2.9,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858487","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}