Wave Motion最新文献_第2页

New integrable (2+1)-dimensional generalized extended kadomtsev-Petviashvili equation 新的可积（2+1）维广义扩展kadomtsev-Petviashvili方程

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-25 DOI: 10.1016/j.wavemoti.2025.103693

Sijie Mao, Maohua Li

The integrable form and diverse exact solutions of the

(2 + 1)

-dimensional generalized extended Kadomtsev-Petviashvili equation are systematically investigated in this paper. Employing Painlevé analysis and the WTC-Kruskal method for the first time, we rigorously confirm the complete integrable form of this equation. By using the Hirota bilinear method, we systematically derive explicit N-soliton solutions and higher-order breather solutions. This foundation facilitates the construction of periodic solutions and novel hybrid states incorporating periodic waves, breather solutions and soliton solutions. Furthermore, asymptotic analysis of N-soliton solutions under the long-wave limit yields spatially localized lump solutions and rogue waves. A significant advancement is the derivation of semi-rational solutions combining lumps, rogue waves, soliton solutions and breather solutions, substantially extending the known solution spectrum for this system. To characterize nonlinear dynamics, we employ three-dimensional visualizations and density plots with contour overlays, clearly elucidating the distinct evolution patterns exhibited by each solution class.

本文系统地研究了（2+1）维广义扩展Kadomtsev-Petviashvili方程的可积形式和多种精确解。首次采用painlev分析和WTC-Kruskal方法，严格地证实了该方程的完全可积形式。利用Hirota双线性方法，系统地导出了n孤子解和高阶呼吸解。这个基础有助于构建周期解和包含周期波、呼吸解和孤子解的新型混合态。此外，对长波极限下n孤子解的渐近分析得到了空间局域块解和异常波。一个重要的进步是推导了结合团块解、异常波解、孤子解和呼吸解的半有理解，大大扩展了该系统的已知解谱。为了表征非线性动力学，我们采用三维可视化和密度图与轮廓叠加，清楚地阐明了不同的演化模式，展示了每个解类。

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引用次数: 0

Optical solitons, dynamic behaviors, and chaotic characteristics of the stochastic fourth-order nonlinear Schrödinger equation with white noise 具有白噪声的随机四阶非线性Schrödinger方程的光学孤子，动态行为和混沌特性

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-25 DOI: 10.1016/j.wavemoti.2025.103694

Ke-Yu Ren

This study investigates the bifurcation and chaotic behaviors of soliton solutions for the stochastic nonlinear Schrödinger equation (NLSE) with fourth-order perturbations. A trial function method is employed to transform the model into an integrable system, yielding a planar nonlinear system. Phase portrait analysis reveals the existence of bright, dark, and kink soliton solutions in the equation. Incorporating external perturbation terms induces chaotic behaviors in the system, with the intensity strongly dependent on perturbation parameters. Based on this finding, stable control of the system’s dynamical behaviors can be achieved through parameter regulation, demonstrating the potential robustness of the model in practical applications. To validate these conclusions, the complete polynomial discriminant system is utilized for the comprehensive classification of exact solutions, and the classification results are mutually corroborated with the previous phase portrait analysis. Notably, the influence of delay effects induced by white noise on soliton amplitude and its mean value is intuitively illustrated through diagrams. To the best of our knowledge, this constitutes the first investigation into the chaotic behaviors of the stochastic extended NLSE with fourth-order perturbations, filling a significant gap in the current research on such models.

研究了具有四阶扰动的随机非线性Schrödinger方程（NLSE）的孤子解的分岔和混沌行为。采用试函数法将模型转化为可积系统，得到平面非线性系统。相像分析揭示了方程中存在亮孤子解、暗孤子解和扭结孤子解。引入外部扰动项会引起系统的混沌行为，其强度强烈依赖于扰动参数。基于这一发现，可以通过参数调节实现对系统动态行为的稳定控制，证明了该模型在实际应用中的潜在鲁棒性。为了验证这些结论，利用完全多项式判别系统对精确解进行全面分类，并将分类结果与前面的相位肖像分析相印证。值得注意的是，白噪声引起的延迟效应对孤子振幅及其平均值的影响通过图表直观地说明。据我们所知，这是对四阶扰动下随机扩展NLSE混沌行为的首次研究，填补了目前这类模型研究的重大空白。

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引用次数: 0

Quasi-continuum approximations for nonlinear dispersive waves in general discrete conservation laws 一般离散守恒律下非线性色散波的准连续统逼近

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-25 DOI: 10.1016/j.wavemoti.2025.103695

Su Yang

In this paper, we study a non-integrable discrete lattice model which is a variant of an integrable discretization of the standard Hopf equation. Interestingly, a direct numerical simulation of the Riemann problem associated with such a discrete lattice shows the emergence of both the dispersive shock wave (DSW) and rarefaction wave (RW). We propose two quasi-continuum models which are represented by partial differential equations (PDEs) in order to both analytically and numerically capture the features of the DSW and RW of the lattice. Accordingly, we apply the DSW fitting method to gain important insights and provide theoretical predictions on various edge features of the DSW including the edge speed and wavenumber. Meanwhile, we analytically compute the self-similar solutions of the quasi-continuum models, which serve as the approximation of the RW of the lattice. We then conduct comparisons between these numerical and analytical results to examine the performance of the approximation of the quasi-continuum models to the discrete lattice.

本文研究了一种非可积离散格模型，它是标准Hopf方程的可积离散化的一种变体。有趣的是，与这种离散晶格相关的黎曼问题的直接数值模拟显示了色散激波（DSW）和稀疏波（RW）的出现。我们提出了用偏微分方程（PDEs）表示的两种准连续体模型，以便在解析和数值上捕捉晶格的DSW和RW的特征。因此，我们应用DSW拟合方法来获得DSW的各种边缘特征（包括边缘速度和波数）的重要见解并提供理论预测。同时，我们解析地计算了拟连续统模型的自相似解，作为晶格RW的逼近。然后，我们将这些数值结果与解析结果进行比较，以检验准连续统模型对离散晶格的近似性能。

引用次数: 0

Study of low-frequency bandgap and vibration attenuation mechanism of multi-meander ligament structures 多曲韧带结构低频带隙及减振机理研究

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-11 DOI: 10.1016/j.wavemoti.2025.103692

Taotao Liu , Zhaozhan Zhang , Anshuai Wang , Yongtao Sun , Qian Ding , Zheyang Hong , Zhixia Wang , Zhichang Qin , Yansen Wu

This paper presents a novel multi-meander ligament structure (MMLS) for low-frequency vibration attenuation. Based on Bloch’s theory and the finite element method, the infinite periodic MMLS (unit cell: lattice constant 62 mm, ligament width 1 mm, filling factor 8.3 %; material: Visijet M3 Crystal, E = 1.463 GPa, ν=0.33, ρ=1020 kg/m³) exhibits 8 bandgaps below 500 Hz, with 42.5 % coverage. The first bandgap spans 61.2–81.0 Hz (19.8 Hz width), and the 6th (358.7–447.3 Hz) is the widest (88.6 Hz). Vibration mode analysis reveals torsional resonance of cross-shaped/straight ligaments drives bandgap formation. For finite periodic arrays (9 × 3 unit cells), frequency response calculations show a peak attenuation of −278.93 dB at 425 Hz, with the lowest bandgap (61.2–81.0 Hz) reaching −98.0 dB. Finally, the propagation characteristics of elastic waves in this structure were analyzed from multiple angles, including group velocity and phase velocity. Overall, this structure not only exhibits excellent vibration reduction performance in the low-frequency range but also has the advantages of being lightweight and easy to fabricate. It provides new ideas for the design of locally resonant acoustic metamaterials.

本文提出了一种新型的多曲曲韧带结构（MMLS），用于低频振动的衰减。基于Bloch理论和有限元方法，无限周期MMLS（单位胞：晶格常数62 mm，韧带宽度1 mm，填充系数8.3%；材料：Visijet M3晶体，E = 1.463 GPa, ν=0.33, ρ=1020 kg/m³）在500 Hz以下有8个带隙，覆盖率为42.5%。第一个带隙的宽度为61.2-81.0 Hz (19.8 Hz)，第6个带隙（358.7-447.3 Hz）最宽（88.6 Hz）。振动模态分析表明，交叉/直韧带的扭转共振驱动带隙的形成。对于有限周期阵列（9 × 3单元格），频率响应计算表明，425 Hz时的峰值衰减为−278.93 dB，最低带隙（61.2-81.0 Hz）达到−98.0 dB。最后，从群速度和相速度等多角度分析了弹性波在该结构中的传播特性。总体而言，该结构不仅在低频范围内具有优异的减振性能，而且具有重量轻、易于制造的优点。这为局部共振声学超材料的设计提供了新的思路。

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引用次数: 0

Rogue wave solutions and modulational instability of a (3+1)-dimensional integrable nonlinear evolution equation （3+1）维可积非线性演化方程的突变波解和调制不稳定性

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-11 DOI: 10.1016/j.wavemoti.2025.103691

Keerthana N, Annapoorani N

Rogue waves, highly localized and transient wave structures of large amplitude, play a critical role in nonlinear dispersive systems such as fluid dynamics, optics, and geophysical flows. This study examines a novel

(3 + 1)

-dimensional nonlinear evolution equation that admits center controlled rogue wave solutions. Integrability is verified using the Painlevé test, confirming the existence of the Painlevé property under suitable parameter constraints. A Cole—Hopf transformation is applied to derive a bilinear form of the equation, enabling the systematic construction of rational rogue wave solutions through polynomial-based auxiliary functions. The resulting first order, second order, and third order solutions display complex localized structures, with their spatial positioning governed by tunable center parameters λ and σ. To establish the physical basis of these solutions, a modulational instability analysis is conducted on a uniform background. The instability spectrum reveals parameter regimes where perturbations grow exponentially, supporting the emergence of rogue waves and confirming consistency with the constructed solution scales. Surface and contour plots are presented to illustrate the spatial complexity and amplification behavior of the solutions. The work introduces a novel framework for center-controlled rogue wave generation, unifying bilinear transformation techniques with spectral stability analysis in a higher-dimensional setting.

异常波是一种高度局域化的大振幅瞬态波结构，在流体动力学、光学和地球物理流等非线性色散系统中起着至关重要的作用。本文研究了一种新的（3+1）维非线性演化方程，该方程允许中心控制的异常波解。利用painlev检验验证了可积性，证实了在适当的参数约束下painlev性质的存在性。应用Cole-Hopf变换推导出方程的双线性形式，从而可以通过基于多项式的辅助函数系统地构造有理的异常波解。得到的一阶、二阶和三阶解显示出复杂的局域结构，其空间定位由可调谐的中心参数λ和σ控制。为了建立这些解的物理基础，在均匀背景下进行了调制不稳定性分析。不稳定谱揭示了扰动呈指数增长的参数状态，支持异常波的出现，并证实了与构建的解尺度的一致性。用曲面和等高线图来说明解的空间复杂性和放大特性。该工作介绍了一种新的中心控制异常波产生框架，将双线性变换技术与高维环境下的光谱稳定性分析统一起来。

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引用次数: 0

Stroh formalism for rotating functionally graded piezo-composite layered waveguide with non-ideal interface 旋转非理想界面功能梯度压电复合层状波导的Stroh形式

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-11 DOI: 10.1016/j.wavemoti.2025.103690

Santan Kumar , Kartik Paul , Richa Kumari

This study investigates the propagation characteristics of Rayleigh-type wave (RTW) in a rotating structure consisting of a dissimilar functionally graded piezoelectric-orthotropic (FGPO) substrate underlying a FGPO layer. The analysis considers the effect of bonding imperfections at the interface between the substrate and the overlying layer. Utilizing the Stroh formalism technique, this study aims to obtain the exact secular relations for the wave propagating in the considered structure under both electrically open (EO) and electrically short (ES) surface conditions. Various cases are examined and discussed based on the derived secular relations. When the relevant parameters are appropriately substituted, the established secular relations align with the existing results in the literature. Additionally, a numerical simulation is performed to graphically illustrate the impacts of wave number, rotation, gradient parameters, mechanical and electrical imperfect parameters, and piezoelectric coupling parameters on the phase velocity (PhV) of the propagating wave in the considered structure for electrical surface conditions. A comparative study among electrically open and short conditions is effectuated considering distinct aspects of the considered geometrical model. This comprehensive analysis provides valuable insights into how aforementioned affecting factors significantly influence RTW propagation in a rotating distinct FGPO layered structure with interfacial imperfection. The reported consequences may be applied in the design of surface acoustic wave (SAW) devices.

本研究研究了瑞利型波（RTW）在由FGPO层下的不同功能梯度压电正交异性（FGPO）衬底组成的旋转结构中的传播特性。分析中考虑了基板与上覆层界面处的键合缺陷的影响。利用Stroh形式技术，本研究旨在获得在电开（EO）和电短（ES）表面条件下在所考虑的结构中传播的波的精确长期关系。根据推导出的世俗关系，对各种情况进行了检验和讨论。当适当替换相关参数时，建立的世俗关系与文献中的现有结果一致。此外，通过数值模拟，图形化地说明了波数、旋转、梯度参数、机电不完善参数和压电耦合参数对电表面条件下所考虑的结构中传播波的相速度（PhV）的影响。考虑到所考虑的几何模型的不同方面，对电气开放和短路条件进行了比较研究。这项综合分析为上述影响因素如何显著影响具有界面缺陷的旋转独特FGPO层状结构中的RTW传播提供了有价值的见解。所报道的结果可应用于表面声波（SAW）器件的设计。

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引用次数: 0

Dark solitons in the defocusing nonlinear Schrödinger equation with quintic terms on elliptic periodic wave background and inelastic collisions 椭圆周期波背景和非弹性碰撞下的五次非线性解焦Schrödinger方程中的暗孤子

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-08 DOI: 10.1016/j.wavemoti.2025.103689

Hanyu Wei , Xin Wang , Tengjin Zhao

In this paper, we study dark solitons on elliptic periodic wave background and their inelastic collisions in the defocusing quintic equation of the nonlinear Schrödinger hierarchy, which consists of fifth-order dispersion and matching nonlinear terms. By virtue of the modified squared wavefunction approach, we obtain the one-phase periodic solution in terms of Jacobi’s elliptic function, and solve the associated linear matrix eigenvalue problem with the elliptic function initial solution. Resorting to the shift formulas between elliptic functions and theta functions as well as the addition formulas of theta functions, we utilize the theta functions to represent these Jacobi’s elliptic function solutions. Using the Darboux transformation and limit technique, we construct the N-elliptic-dark soliton solution expressed in theta functions. Particularly, the explicit one-elliptic-dark soliton solution and its asymptotic behaviors are presented. It is observed that, the fifth-order dispersion and matching nonlinear terms could affect the velocity of solitons. Furthermore, the two- and three-elliptic-dark soliton solutions are illustrated graphically. The fifth-order dispersion and matching nonlinear terms are shown to primarily produce the compression effect on the spatiotemporal distributions of the elliptic dark solitons. Unlike the usual solitons on zero or plane-wave background, collisions involving two or three dark solitons on elliptic periodic wave background presented in this paper are demonstrated to be inelastic, since the amplitudes and shapes of them are changed after interactions. This property of inelastic collision are further confirmed through the standard asymptotic analysis method and some typical numerical plots.

本文研究了椭圆周期波背景下的暗孤子及其在由五阶色散和匹配非线性项组成的非线性Schrödinger离焦五次方程中的非弹性碰撞。利用改进的平方波函数方法，得到了Jacobi椭圆函数的一相周期解，并利用椭圆函数初解求解了相关的线性矩阵特征值问题。利用椭圆函数与函数之间的移位公式以及函数的加法公式，利用函数来表示雅可比椭圆函数的解。利用达布变换和极限技术，构造了用函数表示的n -椭圆-暗孤子解。特别地，给出了显式的单椭圆暗孤子解及其渐近性质。观察到，五阶色散和匹配的非线性项会影响孤子的速度。此外，图解地说明了两个和三个椭圆暗孤子的解。五阶色散和匹配的非线性项对椭圆型暗孤子的时空分布产生压缩效应。与通常的零波或平面波背景下的孤子不同，本文提出的椭圆周期波背景下涉及两个或三个暗孤子的碰撞是非弹性的，因为它们的振幅和形状在相互作用后会发生变化。通过标准渐近分析方法和一些典型数值图进一步证实了非弹性碰撞的这一性质。

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引用次数: 0

Nonlinear surface waves in a piezo-thermoelastic half-space with temperature-dependent dielectric moduli in dual-phase-lag 双相位滞后中介电模量随温度变化的压电-热弹性半空间中的非线性表面波

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-12-04 DOI: 10.1016/j.wavemoti.2025.103688

A.A. Youssef , N.K. Amein , F.A. Salama , A.F. Ghaleb , Ethar A A Ahmed

This paper studies the nonlinear behavior of Rayleigh surface waves in a piezo-thermoelastic half-space under the framework of the dual-phase-lag (DPL) theory. The nonlinearity arises from the temperature dependence of the dielectric moduli, which leads to coupled electro-thermo-mechanical interactions. The governing equations are solved analytically using a perturbation technique up to the second-order approximation, revealing the generation of higher-order harmonics. Numerical simulations demonstrate how thermal relaxation times and dielectric nonlinearity affect the surface wave characteristics. The findings are relevant to wave propagation in functional materials with temperature-dependent electromechanical properties and are important for applications in surface acoustic wave (SAW) devices and thermo-sensitive smart systems.

本文在双相位滞后理论的框架下，研究了压电热弹性半空间中瑞利面波的非线性行为。非线性是由介电模量的温度依赖性引起的，这导致了耦合的电-热-机械相互作用。利用二阶近似的摄动技术解析求解了控制方程，揭示了高次谐波的产生。数值模拟显示了热松弛时间和介电非线性对表面波特性的影响。这些发现与具有温度依赖性机电特性的功能材料中的波传播有关，对于表面声波（SAW）器件和热敏智能系统的应用具有重要意义。

引用次数: 0

A dual-triple combination characteristic line method for stress wave propagation across the Intact-Defected-Intact (IDI) composite strata 完整-缺陷-完整（IDI）复合地层应力波传播的双-三组合特征线法

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-11-28 DOI: 10.1016/j.wavemoti.2025.103687

H.Y. Chen , Q.H. Yang , G.Y. Li , L.F. Fan , M. Wang

A dual-triple combination characteristic line method was proposed to study stress wave propagation through Intact-Defected-Intact (IDI) composite strata. A separated diamond element based on dual-triple combination characteristic lines was introduced to study the stress wave propagation between the intact rock and the defective rock mass. An elastic-viscoelastic combination model was adopted to equivalently study the stress wave propagation through the IDI composite strata. The present method was compared with the traditional method, which employs the elastic models. Subsequently, the stress wave with different incident waveforms (such as half-sinusoidal, rectangular, triangular and explosion shock waves) propagation through IDI composite strata was systematically analyzed. The effect of the incident waveform on the transmission coefficient was discussed. Results indicate that the amplitudes of transmitted waves predicted by the present method were smaller than those obtained by traditional methods. The amplitude of the transmitted wave is largest in the case of the rectangular wave and smallest in the case of the right-triangular wave. The present method efficiently considers the effects of different mechanical properties of various strata on wave propagation with different incident waveforms.

提出了一种双-三组合特征线法研究应力波在完整-缺陷-完好（IDI）复合地层中的传播。引入一种基于双-三组合特征线的分离金刚石元，研究完整岩体与缺陷岩体之间的应力波传播。采用弹性-粘弹性组合模型等效研究了应力波在IDI复合地层中的传播。将该方法与采用弹性模型的传统方法进行了比较。随后，系统分析了不同入射波形（如半正弦、矩形、三角形和爆炸冲击波）的应力波在IDI复合地层中的传播。讨论了入射波形对透射系数的影响。结果表明，该方法预测的透射波振幅比传统方法预测的要小。在矩形波的情况下，透射波的振幅最大，而在直角三角形波的情况下，透射波的振幅最小。该方法有效地考虑了不同地层的不同力学性质对不同入射波形下波浪传播的影响。

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引用次数: 0

Searching for traveling wave solutions in inhomogeneous moving media by factorizing the wave equation 用波方程分解法求非齐次运动介质中的行波解

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-11-24 DOI: 10.1016/j.wavemoti.2025.103678

Semyon Churilov

Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually no reflection or scattering. If the corresponding linear wave equation admits factorization, at least one of the waves it describes propagates without reflection. The paper is devoted to searching for conditions under which both solutions of a one-dimensional factorized wave equation of the second order describe traveling waves, that is, waves propagating without reflection. Possible variants of wave structure are found and the results are compared with those obtained in previous studies.

波浪长距离传输能量是许多自然过程的关键机制。当非均匀介质以这样一种方式排列时，它使特定类型的波传播几乎没有反射或散射，这就成为可能。如果相应的线性波动方程允许因式分解，则它所描述的波中至少有一个不反射地传播。研究一维二阶分解波动方程的两个解都能描述行波的条件，即无反射传播的波。发现了波浪结构的可能变化，并将结果与以往的研究结果进行了比较。

引用次数: 0