Wave Motion最新文献_第4页

State transition and branch structure dynamics of localized waves for the (2+1)-dimensional Fokas system in optical fibers 光纤中（2+1）维Fokas系统局域波的状态跃迁和分支结构动力学

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-13 DOI: 10.1016/j.wavemoti.2025.103656

Zhonglong Zhao , Lihan Zhang , Yong Chen

To explain the formation mechanism of extreme events such as ocean rogue waves and light pulse train excitation, under investigation in this paper is the (2＋1)-dimensional Fokas system, which is considered as the propagation model of nonlinear waves in optical fibers. By applying the complex conjugate condition to the N-soliton solutions, the breather solutions are gained. Breathers can be transformed into nonlinear waves, which is known as state transition. By controlling the wave number ratio, five types of transformed waves are studied, including quasi-soliton, W-typed quasi-periodic wave, M-typed soliton, oscillation M-shaped soliton and multi-peak soliton. The Riemannian circle is introduced to present the gradient relationship of transformed nonlinear waves. When the phase shift produced by the elastic collision of two-soliton or two-breather is large but limited, the two V-shaped structures of two-soliton or two-breather have significantly separated, accompanied by the formation of a branch connecting the two V-shaped solitons. Two quasi-resonant interactions, namely weakly quasi-resonance and strongly quasi-resonance are investigated. Based on the asymptotic analysis method, the properties of the resonant branch are analyzed in detail, including the trajectory, amplitude and velocity. Moreover, the intermediate resonant branch is a new branch generated due to the increase of phase shift, which exhibits temporal invariance and spatial locality. By introducing the small parameter

κ

, the length of the intermediate resonant branch is studied. These results are not only foundational for understanding nonlinear wave dynamics in the Fokas system but also offer critical insights into extreme event formation across disciplines. They explain rogue wave generation in fluids, light pulse anomalies in optical fibers and wave behaviors in shallow water theory. The findings bridge mathematical integrability and physical phenomena, providing a universal framework for analyzing localized wave transitions and resonant interactions in high-dimensional nonlinear systems.

为了解释海洋异常波和光脉冲串激发等极端事件的形成机制，本文研究了非线性波在光纤中的传播模型（2+1）维Fokas系统。通过对n孤子解应用复共轭条件，得到了呼吸解。呼吸可以转化为非线性波，这被称为状态转换。通过控制波数比，研究了拟孤子、w型准周期波、m型孤子、振荡m型孤子和多峰孤子等5类变换波。引入黎曼圆来表示变换后的非线性波的梯度关系。当双孤子或双呼吸子弹性碰撞产生的相移较大但有限时，双孤子或双呼吸子的两个v型结构明显分离，并形成连接两个v型孤子的分支。研究了弱拟共振和强拟共振两种准共振相互作用。基于渐近分析方法，详细分析了谐振支路的轨迹、振幅和速度等特性。中间共振支路是由于相移增加而产生的新支路，具有时间不变性和空间局部性。通过引入小参数κ，研究了中间谐振支路的长度。这些结果不仅为理解Fokas系统中的非线性波动动力学奠定了基础，而且为跨学科的极端事件形成提供了重要见解。他们解释了流体中异常波的产生、光纤中的光脉冲异常以及浅水理论中的波动行为。这些发现在数学可积性和物理现象之间架起了桥梁，为分析高维非线性系统中的局域波跃迁和共振相互作用提供了一个通用框架。

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引用次数: 0

Wave energy dissipation and Bragg scattering by multiple non-uniform porous piers placed over an infinite trench bottom 无限海沟底部多个非均匀多孔桥墩的波能耗散和布拉格散射

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-11 DOI: 10.1016/j.wavemoti.2025.103653

Mampi Majhi , Gour Das , Rumpa Chakraborty

A semi-analytic model that indicates wave energy dissipation due to submerged porous piers with varying porosity placed over an uneven ocean bed is presented here. An infinite trench is present in the ocean bed. The oblique wave interaction with porous barriers and an infinite trench helps to reduce wave loads on shorelines by allowing water to pass through them. Presuming two-dimensional linear wave theory, the matched eigenfunction expansion method, followed by the multi-term Galerkin approximation, is considered to solve the boundary value problem. In Galerkin approximation, the basis functions are chosen in terms of orthogonal and simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions of the barriers and trench edges. The sensitivity of wave reflection and transmission to structural parameters is analyzed. Due to the presence of multiple barriers and trench bottom together, Bragg resonance phenomena in the reflection curve are seen in the energy reflection coefficient, and these phenomena are depicted graphically. A new mathematical form of the energy identity has been derived, which involves a constant term and an energy loss term that occurs due to the present structure. The computed numerical results for physical quantities, viz., reflection and transmission coefficients, energy dissipation, wave force, fluid velocity, and the free surface elevation, are graphically depicted for various values of several parameters. Also, the present results are validated against using the energy identity and the results presented in the existing literature. One special case, when trench depth is finite, the energy coefficient is evaluated and explained graphically. The present study is likely to be of immense importance in the design of breakwaters as a combination of permeable barriers and trench for protecting coastal infrastructures.

本文提出了一种半解析模型，该模型表明波浪能量耗散是由放置在不均匀海床上的具有不同孔隙率的水下多孔墩引起的。海底有一条无限大的海沟。斜波与多孔屏障和无限沟槽的相互作用有助于减少海岸线上的波浪载荷，因为水可以通过它们。假设二维线性波理论，采用匹配特征函数展开法，然后采用多项伽辽金近似来求解边值问题。在伽辽金近似中，基函数是用正交多项式和简单多项式乘以适当的权函数来选择的，权函数的形式由障碍物和沟槽边缘的边缘条件决定。分析了波的反射和透射对结构参数的敏感性。由于多势垒和沟底共同存在，在能量反射系数中可以看到反射曲线中的布拉格共振现象，并将这些现象用图形表示出来。导出了一种新的能量恒等式的数学形式，它包括一个常数项和一个由于现有结构而产生的能量损失项。计算的物理量，即反射和透射系数、能量耗散、波浪力、流体速度和自由面高程的数值结果，以图形形式描述了几个参数的不同值。此外，利用能量同一性和现有文献中的结果验证了本文的结果。当沟深有限时，对能量系数进行了计算，并给出了图解说明。本研究可能对防波堤的设计具有重要意义，防波堤是保护沿海基础设施的可渗透屏障和壕沟的组合。

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引用次数: 0

Model study of ocean wave propagation through broken sea ice covers with variable ice concentration 变冰浓度下海浪通过破碎海冰传播的模式研究

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-11 DOI: 10.1016/j.wavemoti.2025.103655

Jordan P.A. Pitt , Luke G. Bennetts

A theoretical model is used to study the propagation of water waves into and through the marginal ice zone. The marginal ice zone is modelled as a region composed of thin floating elastic plates separated by open water gaps, with randomly chosen lengths. The impact of the marginal ice zone on incoming waves is determined using a reconstruction of the dominant wavelength and attenuation rate, and a transferred amplitude (measuring the change in amplitude at the ice edge), and these quantities are studied for different ice concentrations (the areal fraction of ice cover to open water). For all concentrations, the model is shown to predict a deterministic limit for ice covers composed of floes and gaps much smaller than wavelengths, where the wave fields are independent of the particular realisation of the ice cover and insensitive to further reduction in floe and gap lengths (called the small floe–gap limit). The obtained small floe–gap limit is replicated by using a periodic ice cover that supports damped Bloch waves. The model predicts that as concentration decreases, the wavelength increases and the transferred amplitude and attenuation rate decrease, with attenuation rate scaling with ice concentration.

用理论模型研究了水波进入和穿过边缘冰带的传播。边缘冰带被模拟为一个由开放的水隙分隔的弹性薄板组成的区域，其长度随机选择。边缘冰带对入射波的影响是通过对主导波长和衰减率的重建以及传递振幅（测量冰边缘的振幅变化）来确定的，并对不同冰浓度（冰盖与开放水域的面积比例）的这些量进行了研究。对于所有浓度，该模型显示可以预测由远小于波长的浮冰和缝隙组成的冰盖的确定性极限，其中波场与冰盖的特定实现无关，并且对浮冰和缝隙长度的进一步减少不敏感（称为小浮冰缝隙极限）。通过使用支持阻尼布洛赫波的周期性冰盖来复制所获得的小冰隙极限。模型预测，随着冰浓度的降低，波长增加，传递振幅和衰减率减小，衰减率随冰浓度的增加而减小。

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引用次数: 0

Compressive and shear wave propagation in viscoelastic solid medium as a consequence of prescribed initial displacement fields 在规定的初始位移场作用下，压缩波和剪切波在粘弹性固体介质中的传播

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-11 DOI: 10.1016/j.wavemoti.2025.103651

Slađan Jelić , Dušan Zorica

The propagation of compressive and shear waves through a homogeneous, isotropic, and infinite three-dimensional viscoelastic body is presented through the time evolution of spatial distribution of displacement field, obtained by solving the system of fractional partial differential equations, consisting of the equation of motion of a three-dimensional solid body, the infinitesimal strain tensor, and the fractionally generalized Hooke’s law for a three-dimensional isotropic and elastic body as a constitutive equation, for initial conditions prescribed through the Gaussian function, so that the compressive and shear components of displacement field are expressed as the action of the resolvent tensor on the initial conditions. The graphical representation of displacement field’s compressive and shear component time evolution shows that during a certain time after the excitation there are no qualitative differences between wave propagation through an elastic and a viscoelastic body, regardless whether the wave propagation speed is infinite or finite, while as time increases, differences are firstly observed between elastic and viscoelastic waves, and subsequently between viscoelastic waves with infinite and finite wave propagation speed. The graphical representation of time evolution of spatial profiles of Green’s function, representing a crucial term in the resolvent tensor and containing information about the mechanical characteristics of the material, is revisited due to the applied approach of Fourier and Laplace transform inversions’ order.

通过求解分数阶偏微分方程组得到的位移场空间分布的时间演化，给出了压缩波和剪切波在均匀的、各向同性的无限三维粘弹体中的传播。该系统由三维固体运动方程、无穷小应变张量、将三维各向同性弹性体的分数型广义胡克定律作为本构方程，用高斯函数规定初始条件，从而将位移场的压缩和剪切分量表示为解析张量对初始条件的作用。位移场压缩和剪切分量时间演化的图形表示表明，在激发后的一定时间内，无论波的传播速度是无限还是有限，波在弹性和粘弹性体中的传播没有质的区别，而随着时间的增加，弹性波和粘弹性体之间首先出现了差异。然后在无限和有限波传播速度的粘弹性波之间。由于傅里叶变换和拉普拉斯变换反序的应用方法，格林函数空间轮廓的时间演变的图形表示，代表了解决张量中的一个关键项，包含了关于材料力学特性的信息。

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引用次数: 0

Breather dynamics and the role of near-neighbor coupling in charge transport within the Holstein-SSH DNA model 在Holstein-SSH DNA模型中，呼吸动力学和近邻耦合在电荷输运中的作用

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-11 DOI: 10.1016/j.wavemoti.2025.103652

A. Dang Koko , R.Y. Ondoua , R. Abouem A. Ribama , C.B. Tabi , H.P. Ekobena Fouda , J.P. Nguenang

In this study, we analyze charge transport in the Holstein-SSH DNA lattice model through the analysis of breather dynamics. Using an empirical Holstein-SSH DNA lattice model combined with the quasi-discrete approximation, we have shown that the dynamics of charge transport can be modeled by the nonlinear Schrödinger equation. Analytical study of the modulational instability (MI) phenomenon, based on this equation, revealed that when the nearest-neighbor transfer integral is high, the system becomes more stable, thus offering better charge transport. Furthermore, numerical analysis of MI revealed that our system admits breather solutions, indicating that the stability/instability dynamics can be influenced by the wave number. Subsequently, we derive the breather-type solution and numerically plot its spatio-temporal evolution. One interesting result of this study is that during charge transport in DNA, we find that high values of nearest-neighbor transfer integral could indicate that solitons are more resistant to perturbations or disorder, allowing localized waves to maintain their shape and energy over longer distances. Which allows us to deduce some biological implications linked to charge transport in DNA.

在本研究中，我们通过呼吸动力学分析荷尔斯坦- ssh DNA晶格模型中的电荷输运。利用经验Holstein-SSH DNA晶格模型结合准离散近似，我们证明了电荷输运动力学可以用非线性Schrödinger方程来建模。基于该方程对调制不稳定性（MI）现象的分析研究表明，当最近邻转移积分高时，系统变得更稳定，从而提供更好的电荷输运。此外，MI的数值分析表明，我们的系统允许呼吸解，表明稳定/不稳定动力学可以受到波数的影响。随后，我们导出了呼吸型解，并对其时空演化进行了数值绘制。这项研究的一个有趣的结果是，在DNA中的电荷传输过程中，我们发现高值的最近邻转移积分可能表明孤子更能抵抗扰动或无序，允许局部波在更长的距离上保持其形状和能量。这让我们可以推断出一些与DNA中的电荷传输有关的生物学含义。

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引用次数: 0

An analysis of solutions derived from a general third-order flow equation of the Kaup-Newell system kap - newell系统一般三阶流动方程解的分析

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-10 DOI: 10.1016/j.wavemoti.2025.103649

Zhi Xin

In this paper, we study a general third-order flow equation of the Kaup-Newell system. By using the Darboux transformation method and the determinant representations of transformation and solutions, several solutions to nonlinear equations have been obtained. Including the single-periodic wave solution, soliton solution, Akhmediev breather, Kuznetsov-Ma breather and rogue wave solution. By analyzing the behavior of the above solutions, we observe that the first-order

q_{x}

term has a rotational effect, which significantly slows down solution collision, ultimately leading to the formation of a single solution.

本文研究了kap - newell系统的一般三阶流动方程。利用达布变换方法和变换与解的行列式表示，得到了几种非线性方程的解。包括单周期波解、孤子解、Akhmediev呼吸器、Kuznetsov-Ma呼吸器和异常波解。通过分析上述解的行为，我们观察到一阶qx项具有旋转效应，它显著减缓了解的碰撞，最终导致单解的形成。

引用次数: 0

Linear propagation of tsunami and acoustic–gravity waves on a sphere: Geometrical focusing and defocusing 海啸和声重力波在球体上的线性传播：几何聚焦和散焦

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-10 DOI: 10.1016/j.wavemoti.2025.103643

Byron Williams , Ali Abdolali , Usama Kadri

This study investigates the propagation of tsunami and acoustic–gravity waves at oceanic scales, accounting for the Earth’s curvature within a linear, potential flow framework. While local, near-field analyses often neglect Earth’s curvature and employ Cartesian or cylindrical coordinate systems, this work utilises spherical coordinates to examine wave behaviour over large distances. The analysis reveals that wave amplitudes experience a defocusing effect as they travel from the source (e.g., the Pole) toward the equator, followed by a focusing effect as they approach the antipodal point beyond the equator. A qualitative comparison is made with the 2022 Hunga Tonga–Hunga Ha’apai volcanic eruption in the South Pacific. The study models surface-gravity (tsunami) waves propagating through a compressible water layer, as well as atmospheric acoustic–gravity waves propagating through the air. The entire analysis is carried out within the framework of linear theory.

本研究调查了海啸和声重力波在海洋尺度上的传播，在线性势流框架内考虑地球的曲率。虽然局部的近场分析经常忽略地球的曲率，并使用笛卡尔或柱坐标系，但这项工作利用球坐标来检查远距离上的波的行为。分析表明，当波幅从源（例如，极点）向赤道传播时，会经历散焦效应，随后当它们接近赤道以外的对映点时，会出现聚焦效应。并与2022年南太平洋Hunga Tonga-Hunga Ha 'apai火山喷发进行了定性比较。该研究模拟了通过可压缩水层传播的表面重力（海啸）波，以及通过空气传播的大气声重力波。整个分析是在线性理论的框架内进行的。

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Comparing lubrication approximation with shallow water equations for viscoplastic flows 粘塑性流动的润滑近似与浅水方程的比较

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-09 DOI: 10.1016/j.wavemoti.2025.103648

David Kibe Muchiri , Mathieu Sellier , James N. Hewett , Miguel Moyers-González , Jérôme Monnier

A formal comparative numerical study of the lubrication approximation and the shallow water equations (SWE) for three-dimensional Herschel–Bulkley viscoplastic flows is presented. The validity limits and predictive capabilities of these models are compared across various flow regimes, i.e., in terms of the aspect ratio, inclination angle, rheological properties, basal slipperiness, and Reynolds, Froude, and Bingham numbers. The models’ abilities to capture flow deflections around obstructions are also evaluated. For validation, both model solutions are compared to dam-break experiments. In contrast to some previous works in the literature, both models are shown to adequately reproduce the experimental data in the low Reynolds number regime. The key difference arises during the early phase of a dam-break, where local Froude numbers are high, with the lubrication approximation appearing to overestimate front positions, whereas the SWE solutions align more closely with experimental observations. Furthermore, SWE provides better predictions of flow perturbations caused by obstructions and basal slipperiness. Overall, due to the inclusion of inertial effects, the present SWE model demonstrates broader predictive capability for viscoplastic flow dynamics than the lubrication approximation. However, both models converge as the inclination, aspect ratio, local perturbations, Froude and Reynolds numbers decrease, and as the Bingham number increases.

对三维Herschel-Bulkley粘塑性流动的润滑近似和浅水方程（SWE）进行了形式化的数值比较研究。这些模型的有效性极限和预测能力在不同的流动状态下进行了比较，即在展弦比、倾角、流变特性、基础滑度以及雷诺兹、弗劳德和宾厄姆数方面。模型捕捉障碍物周围气流偏转的能力也进行了评估。为了验证，将两种模型解与溃坝试验进行了比较。与以前的一些文献相比，这两种模型都能充分再现低雷诺数条件下的实验数据。关键的区别出现在溃坝的早期阶段，当地的弗劳德数很高，润滑近似似乎高估了锋面位置，而SWE解决方案与实验观察更接近。此外，SWE可以更好地预测由障碍物和基底滑动引起的流动扰动。总的来说，由于包含惯性效应，目前的SWE模型比润滑近似具有更广泛的粘塑性流动动力学预测能力。然而，随着倾角、展弦比、局部扰动、弗劳德数和雷诺数的减小以及宾厄姆数的增加，两种模型收敛。

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引用次数: 0

Rogue waves on the periodic background in the (2+1)-dimensional Calogero–Degasperis system （2+1）维Calogero-Degasperis系统周期背景上的流氓波

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-08 DOI: 10.1016/j.wavemoti.2025.103650

Liru Wang, Zhaqilao

In this paper, we investigate the construction of rogue wave solutions for the (2+1)-dimensional Calogero-Degasperis system on periodic backgrounds. By combining the Jacobian elliptic function expansion method, Darboux transformation techniques, and nonlinearization of the Lax pair, we successfully derive exact rogue wave solutions on the Jacobian elliptic function dn and cn backgrounds. Our analysis reveals important relationships among the three potential functions in the system and demonstrates unique dynamic features of interactions between rogue waves and periodic structures in high-dimensional nonlinear settings.

本文研究了周期背景下（2+1）维Calogero-Degasperis系统异常波解的构造。结合雅可比椭圆函数展开法、Darboux变换技术和Lax对的非线性化，成功地导出了雅可比椭圆函数dn和cn背景下的精确异常波解。我们的分析揭示了系统中三个势函数之间的重要关系，并展示了高维非线性环境下异常波与周期结构相互作用的独特动力学特征。

引用次数: 0

General rogue waves, breathers and hybrid structures of the coupled Boussinesq system 耦合Boussinesq体系的一般异常波、呼吸波和杂化结构

IF 2.5 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2025-10-04 DOI: 10.1016/j.wavemoti.2025.103647

Haifang Song, Songlin Zhao, Bo Ren

In this paper, we concentrate on the rogue waves, breathers and hybrid solutions of the coupled Boussinesq system via the Kadomtsev–Petviashvili (KP) hierarchy reduction method. We construct the Gram determinant solutions for a

(2 + 1)

-dimensional bilinear system in the KP hierarchy which can be reduced to the coupled Boussinesq system. By considering the dimension-reduction condition, the general high-order rogue wave solutions expressed by derivatives with respect to parameters

p

and

q

are derived. For simplicity, the expressions of the rogue waves are replaced by purely algebraic ones with the help of the known Schur polynomials. The rogue waves from first till fourth order and their dynamic properties are numerically investigated. The structures of the

N

th-order rogue waves contain

\frac{N (N + 1)}{2}

first-order rogue waves. As more free parameters appear, the number of patterns increases. The breather solutions are obtained through setting specific parameter conditions in soliton solutions. Then first- and second-order breathers are attained and their dynamics are analyzed numerically. Three different arrangements for the first-order breathers as well as three types of second-order breather waves including interacting waves, parallel waves and coincident waves are displayed. The hybrid solutions containing first-order breather as well as first- and second-order solitons are given with dynamic analysis. A similar way can be used to obtain the

N

th-order rogue waves and the

M

th-order breathers. The method used in the paper can be extended to other integrable equations theoretically.

本文利用Kadomtsev-Petviashvili （KP）层次约简方法研究了耦合Boussinesq系统的异常波、呼吸波和混合解。构造了KP层次中（2+1）维双线性系统的Gram行列式解，该系统可简化为耦合的Boussinesq系统。考虑降维条件，导出了关于参数p和q的导数表示的一般高阶异常波解。为简单起见，在已知的舒尔多项式的帮助下，将异常波的表达式替换为纯粹的代数表达式。数值研究了一阶到四阶的异常波及其动力特性。N阶异常波结构包含N(N+1)2个一阶异常波。随着更多自由参数的出现，模式的数量也会增加。通过在孤子解中设置特定的参数条件，得到了呼吸解。得到了一阶和二阶呼吸体，并对其动力学进行了数值分析。显示了一阶呼吸波的三种不同排列以及三种类型的二阶呼吸波，包括相互作用波、平行波和重合波。给出了含一阶呼吸子和一阶、二阶孤子的混合解，并进行了动力学分析。用类似的方法可以得到n阶异常波和m阶呼吸波。本文所采用的方法在理论上可以推广到其他可积方程。

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引用次数: 0