Physica D: Nonlinear Phenomena最新文献

英文中文

Classical-quantum simulation of single and multiple solitons generated from the KdV equation 由KdV方程产生的单孤子和多孤子的经典量子模拟

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-31 DOI: 10.1016/j.physd.2025.135012

Andrea Staino , Frank Gaitan , Biswajit Basu

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.

孤子是稳定的、局部的孤立波，可以在不消散或扩散的情况下保持其形状和速度穿过介质。孤子是非线性科学中的一个重要概念，也是物理学中广泛研究的课题。在非线性光学、等离子体物理、凝聚态物质、流体力学、信息编码与传输等多个领域开展了涉及孤子的实验。设计涉及孤子的实验常常严重依赖于数值模拟来预测系统行为和优化实验参数。这些模拟需要非线性偏微分方程（PDEs）的解析，而这些方程在大多数实际情况下是无法解析解的。另一方面，非线性偏微分方程的数值分辨率在计算上具有挑战性，难以准确捕获孤子动力学、相互作用效应和长期稳定性。因此，构建一个能够提供计算加速的孤子传播量子算法是非常有趣的。文献中已经建立了一种求解非线性偏微分方程的量子算法。该算法已被证明可以为Navier-Stokes和Burgers方程提供二次加速。本文研究了无梯度量子求解器生成孤子解的能力。为了验证该算法，考虑了著名的Korteweg-de Vries （KdV）方程的单孤子解和多孤子解。首先，通过比较由KdV数值积分得到的孤波与相应的解析解，研究了量子解的可靠性。随后，研究了不同初始轮廓孤子的量子赋能出现以及经典孤子已知碰撞特性的恢复。将量子算法的数值模拟结果与精确解和经典解进行了比较，得到了很好的一致性。

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引用次数: 0

Coupled stochastic-statistical equations for filtering multiscale turbulent systems 滤波多尺度湍流系统的耦合随机-统计方程

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-31 DOI: 10.1016/j.physd.2025.135013

Di Qi , Jian-Guo Liu

We present a new strategy for the statistical forecasts of multiscale nonlinear systems involving non-Gaussian probability distributions with the help of observation data from leading-order moments. A stochastic-statistical modeling framework is designed to enable systematic theoretical analysis and support efficient numerical simulations. The nonlinear coupling structures of the explicit stochastic and statistical equations are exploited to develop a new multiscale filtering system using statistical observation data, which is represented by an infinite-dimensional Kalman–Bucy filter satisfying conditional Gaussian dynamics. To facilitate practical implementation, a finite-dimensional stochastic filtering model is proposed that approximates the intractable infinite-dimensional filter solution. We prove that this approximating filter effectively captures key non-Gaussian features, demonstrating consistent statistics with the optimal filter first in its analysis step update, then at the long-time limit guaranteeing stable convergence to the optimal filter. Finally, we build a practical ensemble filter algorithm based on the stochastic filtering model. Robust performance of the modeling and filtering strategies is demonstrated on prototype models, implying wider applications on challenging problems in statistical prediction and uncertainty quantification of multiscale turbulent states.

本文提出了一种利用前阶矩观测数据对非高斯概率分布的多尺度非线性系统进行统计预测的新策略。设计了一个随机统计建模框架，使系统的理论分析和支持有效的数值模拟。利用显式随机方程和统计方程的非线性耦合结构，利用统计观测数据建立了一种新的多尺度滤波系统，该系统由满足条件高斯动力学的无限维卡尔曼-布西滤波器表示。为了便于实际实现，提出了一种有限维随机滤波模型，近似于难以处理的无限维滤波解。我们证明了这种近似滤波器有效地捕获了关键的非高斯特征，首先在其分析步长更新中证明了与最优滤波器的一致统计量，然后在长时间极限上保证了稳定收敛到最优滤波器。最后，基于随机滤波模型构建了一种实用的集成滤波算法。在原型模型上证明了建模和滤波策略的鲁棒性，这意味着在多尺度湍流状态的统计预测和不确定性量化等挑战性问题上有更广泛的应用。

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引用次数: 0

Real-valued vector modified Korteweg–de Vries equation: Solitons featuring multiple poles 实值向量修正Korteweg-de Vries方程：具有多极的孤子

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-31 DOI: 10.1016/j.physd.2025.135009

Zhenzhen Yang , Huan Liu , Jing Shen

We delve into the inverse scattering transform of the real-valued vector modified Korteweg–de Vries equation, emphasizing the challenges posed by

N

pairs of higher-order poles in the determinant of the transmission coefficient and the enhanced spectral symmetry stemming from real-valued constraints. Utilizing the generalized vector cross product, we formulate an

(n + 1) \times (n + 1)

matrix-valued Riemann–Hilbert problem to tackle the complexities inherent in multi-component systems. We subsequently demonstrate the existence and uniqueness of solutions for a singularity-free equivalent problem, adeptly handling the intricacies of multiple poles. In reflectionless cases, we reconstruct multi-pole soliton solutions through a system of linear algebraic equations.

我们深入研究了实值矢量修正Korteweg-de Vries方程的逆散射变换，强调了N对高阶极点对透射系数行列式的挑战以及实值约束增强的光谱对称性。利用广义向量叉积，我们提出了一个（n+1）×（n+1）矩阵值黎曼-希尔伯特问题来解决多组分系统固有的复杂性。我们随后证明了一个无奇点等价问题解的存在性和唯一性，熟练地处理了多极的复杂性。在无反射情况下，我们通过线性代数方程组重构了多极孤子解。

引用次数: 0

Alignment of geophysical fields: A differential geometry perspective 地球物理场对准：微分几何视角

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-30 DOI: 10.1016/j.physd.2025.134997

Yicun Zhen , Valentin Resseguier , Bertrand Chapron

To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimization formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underlying physical processes.

为了估计物理状态变量的位移，必须考虑控制状态变量的物理原理。从技术上讲，对于某一类状态变量，每个状态变量都与一个张量场相关联。位移映射作用于不同状态变量的方式将根据它们相关的不同张量场定义而有所不同。位移过程可以明确地确保某些物理量（总质量、总涡量、总动能等）的守恒，并制定了基于微分几何的优化公式。根据正确的物理变形，只要位移映射是强相关的，就可以合理地将估计的位移映射应用于未观察到的状态变量。这导致了一种新的推动策略，使用所有可用的观察来推断观察到的和未观察到的状态变量的位移。在集成数据同化之前使用所提出的助推方法，数值结果表明底层物理过程的内在结构得到了更好的保存。

引用次数: 0

Corrigendum to “Integrable nonlinear PDEs as evolution equations derived from multi-ion fluid plasma models” [Physica D 472 (2025) 1–10/134527] “可积非线性偏微分方程作为从多离子流体等离子体模型导出的演化方程”的勘误[物理学报D 472 (2025) 1-10/134527]

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-29 DOI: 10.1016/j.physd.2025.134985

Steffy Sara Varghese , Kuldeep Singh , Frank Verheest , Ioannis Kourakis

引用次数: 0

State–Hamiltonian Neural Networks for learning dynamical systems 用于学习动力系统的状态-哈密顿神经网络

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-29 DOI: 10.1016/j.physd.2025.134994

Yan Wu , Hong-Kun Zhang , Huagui Duan

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.

理解动力系统的行为及其潜在的物理定律一直是研究的中心焦点。然而，以前的方法经常受到高数据和计算需求或无法推断潜在物理定律的影响。在本文中，我们提出了一种新的状态-哈密顿神经网络（state - hnn）框架，它可以同时学习从时间到系统状态的映射，并推断潜在的哈密顿动力学。利用哈密顿力学，提出的方法加强了能量守恒，并产生了物理上一致的预测。我们在几个基准系统上对该方法进行了评估：(1)质量-弹簧系统；(2)双摆；(3)单摆；(4)三体系统。我们特别对三体实验进行了详细的分析。结果表明，State-HNN在保持能量不变性的同时准确捕获复杂动态，优于经典的哈密顿神经网络（HNN）方法，特别是在高维环境中。

引用次数: 0

Quasi-breathers in square lattice with long-range interactions 具有长程相互作用的方晶格中的拟呼吸子

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-29 DOI: 10.1016/j.physd.2025.135011

Rita I. Babicheva , Igor A. Shepelev , Evgeny K. Naumov , Daxing Xiong , Aleksey A. Kudreyko , Sergey V. Dmitriev

The phenomenon of energy localization in nonlinear lattices is of interest to both fundamental science and crystal physics. Localized energy can help overcome potential barriers to defect migration or initiation, which is a topic of significant scientific and practical importance. In real lattices, such as crystal lattices, the presence of inevitable perturbations necessitates a shift in research focus from finding exact discrete breather solutions towards the long-lived quasi-breather (qB) solutions. Higher-dimensional lattices support different qBs with different symmetries, and it is important to know the conditions for their existence. In crystals, long-range interactions, such as metallic or Coulomb interactions, can play an important role. In the present work, the search for qBs in the square

β

-FPUT lattice is continued, taking into account interactions up to the fourth neighbor. The search for qBs is carried out under the assumption that the stiffness of the bonds decreases with their length, as is expected for chemical bonds in crystals. New qBs are identified in comparison to the lattice with short interactions, and it is demonstrated that some of them can move along the lattice, transporting energy.

非线性晶格中的能量局域化现象是基础科学和晶体物理学都感兴趣的问题。局部能量可以帮助克服缺陷迁移或启动的潜在障碍，这是一个具有重要科学意义和实际意义的课题。在实际晶格中，如晶格，不可避免的扰动的存在使得研究重点从寻找精确的离散呼吸解转向长寿命的准呼吸（qB）解。高维晶格支持具有不同对称性的不同量子点，了解它们存在的条件是很重要的。在晶体中，远程相互作用，如金属或库仑相互作用，可以发挥重要作用。在目前的工作中，继续在方形β-FPUT晶格中寻找qBs，考虑到第四个邻居的相互作用。qb的搜索是在假设键的刚度随着它们的长度而减小的情况下进行的，正如对晶体中的化学键所期望的那样。与具有短相互作用的晶格相比较，确定了新的量子点，并证明了其中一些量子点可以沿着晶格移动，传递能量。

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引用次数: 0

On the inverse scattering transform for the matrix mKdV equation with multiple higher-order poles 具有多个高阶极点的矩阵mKdV方程的逆散射变换

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-28 DOI: 10.1016/j.physd.2025.135002

Wenjing Xing , Nan Liu , Jinyi Sun

In this study, we present a systematical inverse scattering transform for the matrix modified Korteweg–de Vries (mKdV) equation with the associated analytic scattering coefficients consisting of

N

pairs of higher-order zeros. The analyticity properties and symmetries of the Jost eigenfunctions and scattering coefficients are discussed in the direct problem. In particular, discrete spectrum associated with these

N

pairs of multiple zeros is analyzed explicitly. Next, we formulate a 4 × 4 matrix Riemann–Hilbert (RH) problem that incorporates the residue conditions at these higher-order poles. By solving this RH problem, we obtain the reconstruction formula for the solution of the matrix mKdV equation. Under the reflectionless condition, the associated RH problem can be reduced to a system of linear algebraic equations. We demonstrate that the solution to this system exists and is unique, allowing us to explicitly derive the higher-order soliton solutions.

本文提出了矩阵修正的Korteweg-de Vries （mKdV）方程的系统逆散射变换，该方程的解析散射系数由N对高阶零组成。在直接问题中讨论了约斯特特征函数和散射系数的解析性和对称性。特别地，明确地分析了与这N对多零相关联的离散谱。接下来，我们提出了一个包含这些高阶极点上的剩余条件的4 × 4矩阵黎曼-希尔伯特（RH）问题。通过求解该RH问题，得到了矩阵mKdV方程解的重构公式。在无反射条件下，相关的RH问题可以化为一个线性代数方程组。我们证明了该系统解的存在性和唯一性，从而可以显式地导出其高阶孤子解。

引用次数: 0

Modified physics-informed neural networks: Data-driven rogue-wave dynamics and parameter identifications for the Newell-type long-short wave system 改进的物理信息神经网络：newwell型长短波系统的数据驱动的流氓波动力学和参数识别

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-27 DOI: 10.1016/j.physd.2025.135008

Junchao Chen , Jin Song , Ming Zhong , Zhenya Yan

We, based on the extended physics-informed neural networks (PINNs), propose a stepwise multi-stage training strategy with the U-shaped enveloping domain decomposition, in which the collection points are resampled and the pseudo characteristic points are introduced at the next stage of training, and transfer learning are employed between two successive stages. The modified PINNs approach is used to investigate data-driven rogue-wave dynamics and parameter identifications for the Newell-type long-short wave system. For the forward problems, we effectively learn three types of first- and second-order rogue wave solutions including bright, intermediate and dark states in the short-wave component, which belong to a class of localized solutions with the steep gradients. For the inverse problems, we identify the unknown coefficient parameters with and without noises by using the classical PINNs algorithm. In particular, we introduce the characteristic points as internal information points during the training process to improve the convergence rate and prediction accuracy.

在扩展物理信息神经网络（pinn）的基础上，提出了一种基于u形包络域分解的逐步多阶段训练策略，该策略在下一阶段训练中对采集点进行重采样并引入伪特征点，并在两个连续阶段之间使用迁移学习。利用改进的PINNs方法研究了newwell型长短波系统的数据驱动的流氓波动力学和参数辨识。对于正演问题，我们有效地学习了短波分量中的三种一阶和二阶异常波解，包括亮态、中间态和暗态，它们属于一类具有陡梯度的局部解。对于反问题，我们使用经典的pinn算法识别带和不带噪声的未知系数参数。特别地，我们在训练过程中引入特征点作为内部信息点，提高了收敛速度和预测精度。

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引用次数: 0

On a generalized nonlocal shallow-water equation 一类广义非局部浅水方程

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-10-27 DOI: 10.1016/j.physd.2025.134998

Shijing Gao , Lili Huang , Yunfei Yue

Consideration herein is a quasilinear generalized nonlocal shallow-water equation for moderate-amplitude equatorial waves with the Coriolis and equatorial undercurrent effects, which can be derived from the incompressible and rotational two-dimensional shallow water in equatorial region according to the formal asymptotic procedures. This resulting equation is related to the b-family equation and the compressible hyperelastic rod model in the material science. Subsequently, the blow-up criterion for the established equation in a suitable Sobolev space is presented without the help of conservation law. Moreover, the influences and interactions of the nonlocal higher nonlinearities, vorticity and weak Coriolis force on wave-breaking phenomena are investigated, as well as the persistence properties of the solutions in weighted

L^{p}

spaces. Finally, we provide a sufficient condition for global strong solutions to the generalized nonlocal shallow-water equation in some special case.

本文考虑了一个具有科里奥利效应和赤道暗流效应的中振幅赤道波的拟线性广义非局部浅水方程，该方程可由赤道地区不可压缩和旋转的二维浅水根据形式渐近过程导出。所得方程与材料科学中的b族方程和可压缩超弹性棒模型有关。随后，在不借助守恒律的情况下，给出了所建立方程在合适Sobolev空间中的爆破判据。此外，研究了非局部高非线性、涡度和弱科里奥利力对破波现象的影响和相互作用，以及加权Lp空间中解的持久性。最后，在一些特殊情况下，给出了广义非局部浅水方程全局强解的充分条件。

引用次数: 0

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