Physica D: Nonlinear Phenomena最新文献

Large time and distance asymptotics of the one-dimensional impenetrable Bose gas and Painlevé IV transition

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-27 DOI: 10.1016/j.physd.2025.134589

Zhi-Xuan Meng , Shuai-Xia Xu , Yu-Qiu Zhao

引用次数: 0

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-25 DOI: 10.1016/j.physd.2025.134572

Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo

{"title":"Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems","authors":"Shane A. McQuarrie , Anirban Chaudhuri , Karen E. Willcox , Mengwu Guo","doi":"10.1016/j.physd.2025.134572","DOIUrl":"10.1016/j.physd.2025.134572","url":null,"abstract":"<div><div>This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. We demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134572"},"PeriodicalIF":2.7,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511277","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

Lp stability-based synchronization of delayed multi-weight neural networks under switching topologies

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-22 DOI: 10.1016/j.physd.2025.134577

Yunxiao Jia, Xiaona Yang, Xian Zhang

{"title":"Lp stability-based synchronization of delayed multi-weight neural networks under switching topologies","authors":"Yunxiao Jia, Xiaona Yang, Xian Zhang","doi":"10.1016/j.physd.2025.134577","DOIUrl":"10.1016/j.physd.2025.134577","url":null,"abstract":"<div><div>In this paper, the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization problem of delayed multi-weight neural networks under switching topologies is investigated. The involved delays include time-varying leakage, transmission and distributed delays. Firstly, a novel controller is designed to ensure <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization between the drive and response multi-weight neural networks. Secondly, a property of solutions of the considered error system is investigated, which forms a basis of obtaining a new criterion of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization. In contrast to the existing ones, the obtained criterion comprises just a small number of simple linear scalar inequalities, thereby amount of computations is greatly reduced. Finally, a numerical example related to communication networks is presented to demonstrate the applicability of the obtained <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization criterion. It is worth noting that the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization control problem of delayed multi-weight neural networks under switching topologies is solved for the first time, and the proposed method is directly based on the definitions of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> stability-based synchronization, which is easily extended to some switching delayed system models.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134577"},"PeriodicalIF":2.7,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510672","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

Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134578

Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi

{"title":"Exponential synchronization of high-dimensional Kuramoto models on the complex sphere based on directed graphs","authors":"Xinyun Liu , Wei Li , Xueyan Li , Yushi Shi","doi":"10.1016/j.physd.2025.134578","DOIUrl":"10.1016/j.physd.2025.134578","url":null,"abstract":"<div><div>Synchronization of populations is a common phenomenon in nature. The high-dimensional Kuramoto model is one of the most typical continuous system models for studying synchronization phenomena in multi-individual systems. Due to Lohe’s remarkable work on models of multi-individual systems, the high-dimensional Kuramoto models are also called the Lohe models, and the Lohe Hermitian sphere (LHS) model is a generalization of the Lohe models in the complex space. In this paper, we study the exponential synchronization problem of the LHS models based on directed graphs. By introducing the synchronization error function, we have developed a set of synchronization error dynamic equations for the identical oscillators using matrix Riccati differential equations. The system of synchronization error dynamic equations is studied, a total error function is constructed, and exponential synchronization of the LHS model on the unit complex sphere is demonstrated. An approximate linearization of the error dynamics equations is performed, to obtain the exponential decay rate of the system. For the LHS model with nonidentical oscillators on the unit complex sphere, using the synchronization error function, it is shown that practical synchronization can be achieved when the connection graph of the system is strongly connected.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134578"},"PeriodicalIF":2.7,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510673","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

On periodic solutions for the Maxwell–Bloch equations

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-21 DOI: 10.1016/j.physd.2025.134581

A.I. Komech

引用次数: 0

On the nonexistence of NLS breathers

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-20 DOI: 10.1016/j.physd.2025.134580

Miguel Á. Alejo , Adán J. Corcho

引用次数: 0

Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-19 DOI: 10.1016/j.physd.2025.134579

Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha

{"title":"Existence, stability and nonlinear estimates of stationary-state solutions to the nonlinear aggregation with collision-induced fragmentation model","authors":"Farel William Viret Kharchandy, Vamsinadh Thota, Jitraj Saha","doi":"10.1016/j.physd.2025.134579","DOIUrl":"10.1016/j.physd.2025.134579","url":null,"abstract":"<div><div>Existence and uniqueness of a stationary-state solution to the nonlinear aggregation and collision-induced fragmentation equation is proved over a weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-space. The assumption of a detailed balance condition is relaxed to attain the existence of the solution. Aggregation and fragmentation kernels are considered to exhibit linear and quadratic growth rates respectively which encompass a wide range of physically significant kernels. Asymptotic properties of the time-dependent solution are analyzed in detail and convergence of the same to the stationary-state solution is also examined. Exponential rate of convergence is obtained by proving the asymptotic stability of the stationary-state solution. Further, nonlinear estimates of the solution are obtained using semigroup theory of operators. The study is further extended to analyze the nonexistence of a stationary-state solution for a particular choice of kinetic kernels over a suitably constructed solution space. A numerical example is provided in order to visualize the nonexistence of a stationary-state solution and other physical quantities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134579"},"PeriodicalIF":2.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464731","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

Breathers of the nonlinear Schrödinger equation are coherent self-similar solutions 非线性薛定谔方程的呼吸器是相干自相似解

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-17 DOI: 10.1016/j.physd.2025.134575

Alexey V. Slunyaev

引用次数: 0

Theoretical analysis of the effect of strength on oscillations and Rayleigh-Taylor instabilities on a collapsing spherical surface, supported by a study on Bell-Plesset oscillations

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-15 DOI: 10.1016/j.physd.2025.134588

C.A. Walsh

{"title":"Theoretical analysis of the effect of strength on oscillations and Rayleigh-Taylor instabilities on a collapsing spherical surface, supported by a study on Bell-Plesset oscillations","authors":"C.A. Walsh","doi":"10.1016/j.physd.2025.134588","DOIUrl":"10.1016/j.physd.2025.134588","url":null,"abstract":"<div><div>Small perturbations on a spherical interface, between two materials of different densities, oscillate in amplitude as the radius of the interface increases or decreases. The historical approach to this problem has been to solve Laplace's equation for the velocity potential in the domains on either side of the interface and equate the pressure at the interface. This paper considers the effects of yield strength and shear modulus on oscillations on a collapsing spherical surface between a higher density, strong material, and a lower-density, weak material.</div><div>The strong material is assumed to be incompressible, flow in an elasto-plastic manner and lie on the yield surface. The yield surface is taken to be defined by the von Mises yield criterion and the flow to follow the Prandtl-Reuss rules. The Navier-Stokes equation provides the starting point for the analysis and yields the necessary stress terms for inclusion in Laplace's equation. The analysis is limited to a first-order approximation. The material strength model is assumed to be constant. This paper will outline the theoretical analysis and show a comparison of the analytical results with simulations carried out using a hydrocode. The theoretical analysis will be shown to give good agreement with the calculations over a range of different initial wavelengths and strength parameters. When the yield strength is high, the amplitudes of the oscillations decay monotonically to zero; at even higher yield strengths oscillations are completely inhibited and the amplitudes increase, due to geometric convergence effects. Criteria for these phenomena are derived and shown to agree approximately with calculations made using the theoretical analysis.</div><div>UK Ministry of Defence © Crown Owned Copyright 2024/AWE</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134588"},"PeriodicalIF":2.7,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487671","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

Whitham modulation theory for the discontinuous initial-value problem of the generalized Kaup–Boussinesq equation

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-02-14 DOI: 10.1016/j.physd.2025.134573

Ruizhi Gong, Deng-Shan Wang

{"title":"Whitham modulation theory for the discontinuous initial-value problem of the generalized Kaup–Boussinesq equation","authors":"Ruizhi Gong, Deng-Shan Wang","doi":"10.1016/j.physd.2025.134573","DOIUrl":"10.1016/j.physd.2025.134573","url":null,"abstract":"<div><div>The Whitham modulation theory is developed to investigate the complete classification of solutions to discontinuous initial-value problem of the generalized Kaup–Boussinesq (KB) equation, which can model phenomenon of wave motion in shallow water. According to the dispersion relation, the generalized KB equation includes the generalized good-KB equation and generalized bad-KB equation, respectively. Firstly, the periodic wave solutions and the corresponding Whitham equations associated with the generalized bad-KB equation are given by Flaschka–Forest–McLaughlin approach. Secondly, the basic rarefaction wave structure and dispersive shock wave structure are described by analyzing the zero-genus and one-genus Whitham equations. Then the complete classification of solutions to Riemann problem of the generalized bad-KB equation is provided, and eighteen different cases are classified, including five critical cases. The distributions of Riemann invariants and the evolutions of self-similar states for each component are demonstrated in detail. It is shown that the exact soliton solution is in good agreement with the soliton edge of the modulated dispersive shock wave. Moreover, it is observed that the phase portraits in each case establish a consistent relationship with the behavior of the modulated solutions. Finally, for the generalized good-KB equation, a new type of discontinuous initial-value problem with constant-periodic wave boundaries is explored, and some novel modulated solutions with trigonometric shock waves are found. It is remarked that such trigonometric shock waves are absent in the generalized bad-KB equation because the small amplitude limits of the periodic waves are not trigonometric functions but constants. The results in this work reveal exotic wave-breaking phenomena in shallow water and provide a feasible way to investigate the discontinuous initial-value problem of nonlinear dispersive equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134573"},"PeriodicalIF":2.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420683","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