Wave Motion最新文献

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On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrödinger equations 论一类聚焦非线性薛定谔方程非零背景解的寿命

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-10-11 DOI: 10.1016/j.wavemoti.2024.103419

Dirk Hennig , Nikos I. Karachalios , Dionyssios Mantzavinos , Dimitrios Mitsotakis

The global solvability in time and the potential for blow-up of solutions to non-integrable focusing nonlinear Schrödinger equations with nonzero boundary conditions at infinity present challenges that are less explored and understood compared to the case of zero boundary conditions. In this work, we address these questions by establishing estimates on the lifespan of solutions to non-integrable equations involving a general class of nonlinearities. These estimates depend on the size of the initial data, the growth of the nonlinearity, and relevant quantities associated with the amplitude of the background. The estimates provide quantified upper bounds for the minimum guaranteed lifespan of solutions. Qualitatively, for small initial data and background, these upper bounds suggest long survival times consistent with global existence of solutions. On the other hand, for larger initial data and background, the estimates indicate the potential for the intriguing phenomenon of instantaneous collapse in finite time. These qualitative theoretical results are illustrated via numerical simulations. Furthermore, importantly, the numerical findings motivate the proof of improved theoretical upper bounds that provide excellent quantitative agreement with the order of the numerically identified lifespan of solutions.

与边界条件为零的情况相比，在无限远处边界条件为非零的非可协焦非线性薛定谔方程的解在时间上的全局可解性和炸毁的可能性提出了探索和理解较少的挑战。在这项工作中，我们通过建立对涉及一般非线性的非可协方程的解的寿命的估计来解决这些问题。这些估计值取决于初始数据的大小、非线性的增长以及与背景振幅相关的相关量。这些估计值提供了解的最小保证寿命的量化上限。从定性上讲，对于较小的初始数据和背景，这些上限表明求解的存活时间较长，符合全局存在性。另一方面，对于较大的初始数据和背景，这些估计值表明有可能出现在有限时间内瞬间崩溃的有趣现象。这些定性理论结果通过数值模拟得到了说明。此外，重要的是，数值研究结果促使我们证明了改进的理论上限，这些上限与数值确定的解的寿命阶数具有极好的定量一致性。

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引用次数: 0

Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems 典型时域波散射问题的广义特征函数展开和奇异性展开方法

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-10-11 DOI: 10.1016/j.wavemoti.2024.103421

Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.

应用广义特征函数展开法（GEM）和奇异性展开法（SEM）求解了时域中无限拉伸弦上波散射的典型问题。在没有散射体存在的情况下，GEM 与达朗贝尔公式等价；在点质量散射体与弹簧耦合的情况下，也推导出了 GEM。离散 GEM 是对离散傅立叶变换的概括，证明它可以简化为矩阵乘法。由傅立叶变换和残差定理推导出的 SEM 也被用于解决质量-弹簧系统的散射问题。此外，GEM 和 SEM 还被用于解决与锚点保持固定距离的质量的波散射问题，它支持更复杂的共振行为。

引用次数: 0

Natural frequencies of a Timoshenko beam with cracks 有裂缝的季莫申科梁的自然频率

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-10-06 DOI: 10.1016/j.wavemoti.2024.103420

E.I. Shifrin, I.M. Lebedev

A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.

本研究考虑了计算被有限数量的横向开口裂缝削弱的季莫申科梁的固有频率问题。该问题针对两种已知的裂缝模型进行求解。在一个模型中，每条裂缝都由一个无质量的旋转弹簧模拟。在另一个模型中，每条裂缝都由两个无质量弹簧（一个拉伸弹簧和一个旋转弹簧）模拟。以前成功应用于欧拉-伯努利梁的计算带裂缝振动梁固有频率的有效方法，现在扩展到了季莫申科梁的情况。所开发的方法可以大大降低行列式的阶数，行列式的零点即为自然频率。研究考虑了数值实例。在可能的情况下，将结果与已知结果进行比较。

引用次数: 0

Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system 高阶非线性薛定谔-麦克斯韦-布洛赫系统的周期性背景上的游荡波

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-29 DOI: 10.1016/j.wavemoti.2024.103417

Jian Chang, Zhaqilao

In this paper, we construct the rogue wave solutions on the background of the Jacobian elliptic functions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system. The Jacobian elliptic function traveling wave solutions as the seed solutions are considered. Through the approach of the nonlinearization of the Lax pair and Darboux transformation method, the rogue waves and the line rogue waves on the Jacobian elliptic functions dn and cn background are obtained, respectively.

本文以高阶非线性薛定谔-麦克斯韦-布洛赫（Schrödinger-Maxwell-Bloch）系统的雅各布椭圆函数为背景，构建了流波解。雅各布椭圆函数行波解被视为种子解。通过拉克斯对的非线性化和达尔布克斯变换方法，分别得到了雅各布椭圆函数 dn 和 cn 背景上的流氓波和线流氓波。

引用次数: 0

On the viscoelastic-electromagnetic-gravitational analogy 关于粘弹性-电磁-引力类比

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-19 DOI: 10.1016/j.wavemoti.2024.103411

José M. Carcione , Jing Ba

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.

通过将广义相对论的张量引力方程线性化，并将其转换为与麦克斯韦电磁方程相对应的矢量形式，实现了电磁学与引力之间的类比。在此基础上，我们利用与粘弹性的等价关系，提出了引力波理论。我们在微分方程中加入了一个阻尼项，相当于电磁学中的欧姆定律和粘弹性中的麦克斯韦粘度，用来描述波的衰减。粘弹性中的微分方程是跨平面剪切波的微分方程，通常称为 SH 波。平面波分析给出了相速度、能量速度、场的品质因数和衰减系数以及能量平衡。为了获得这些特性，我们使用了粘弹性的类比方法；电磁波和引力波的特性与剪切波相似。衰减的存在意味着瞬态场通常由不均匀（非均匀）平面波组成，其中传播矢量和衰减矢量不指向同一方向，相位速度矢量和能量通量（能量速度）也不平行。跨平面场的极化是线性的，垂直于传播-衰减平面，而平面内场的极化是椭圆形的。分析时空域中的瞬态波场时，使用了格林函数（在均质介质中）和网格法（在异质介质中），网格法基于计算空间导数的傅立叶伪谱法和计算时间步进的 4 阶 Runge-Kutta 方案。在示例中，考虑了使用四极源在太阳-地球和地球-月球距离上的波传播，并与粘弹性波进行了比较。比较了格林解法和网格解法，以测试后一种算法。最后，介绍了一个在异质介质中传播的例子。

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引用次数: 0

The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory 弛豫对等温声学行波的影响：基于纳维-斯托克斯-麦克斯韦理论的新型可解模型

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103415

P.M. Jordan , A. Puri

An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.

本文分析了麦克斯韦流体的一个特殊子类中的等温声学行波，特别是那些行为类似于完美气体的流体，其中剪切粘度与质量密度的平方成正比。推导并分析了精确解，计算了冲击厚度结果，并验证了等温假设在热力学上与所考虑的马赫数值的一致性。结果表明，在两者都产生分散冲击剖面的范围内，麦克斯韦情况导致的冲击厚度明显小于相应的牛顿（流体）情况导致的非对称解剖面。

引用次数: 0

Solitary wave solutions and their limits to the fractional Schrödinger system 分数薛定谔系统的孤波解及其极限

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103416

Guoyi Fu, Xiaoyan Chen, Shihui Zhu

This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.

本研究关注（2+1）维非线性分数薛定谔系统的孤波解和动力学行为。通过探索相应哈密顿的平衡级的动态特性，得到了上述系统的精确解的表达式，包括孤波解、周期波解、奇异周期波解、奇异波解、扭结波解和反扭结波解。此外，还研究了这些解对非线性分数薛定谔系统的线性稳定性、几何特性和极限行为。

引用次数: 0

New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves 一些 (2+1) 维非线性演化方程和折叠波的新精确解

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103414

Kai Zhou , Sen-Yue Lou , Shou-Feng Shen

By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.

通过广田双线性方法和特殊的多线性变量分离等式，构建了一些 (2+1)-dimensional 非线性演化方程的新的低维任意函数精确解。也就是说，我们提出了一种求解 mNNV 型方程和 Burger 型方程的统一方法。该方法成功的关键因素是我们以任意阶变量分离的形式构建了一些简化的广田双线性计算公式。我们使用适当的多值函数来构建相干结构，如钟型、峰型和环型折叠波。

引用次数: 0

A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure 具有完整科里奥利力和漩涡结构的高维地球物理流体模型

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-14 DOI: 10.1016/j.wavemoti.2024.103410

Na Liu , Xiaojun Yin , Ruigang Zhang , Quansheng Liu

Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.

在此，我们利用加德纳-莫里川坐标变换和扰动法，从涡度方程中提出了一个描述大尺度罗斯比波动态特征的高维模型。为了揭示物理参数对高维模型的影响，我们首先给出了模型的频散关系，并用 Hirota 方法给出了 N-soliton 解。随后，利用长波极限法得出了块解。结果表明，科里奥利力的水平分量对非线性罗斯比波起着强迫作用，并影响着经向结构的振幅。此外，在次级带状基本流背景下，对于不同的块解，流场会出现偶极阻塞或双涡结构。研究还表明，水平科里奥利力只导致涡向纬度方向移动。

引用次数: 0

Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields 强水平电场下具有恒定涡度的周期波下的流动结构

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion

Pub Date : 2024-09-12 DOI: 10.1016/j.wavemoti.2024.103413

Marcelo V. Flamarion , Evgeny Kochurin , Roberto Ribeiro Jr , Nikolay Zubarev

While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves.

虽然已有多篇文章分别论述了电流体动力学（EHD）流动或恒定涡度流动，但人们对 EHD 和恒定涡度的综合效应对流动的影响程度知之甚少。本研究旨在通过研究水平电场和恒定涡度对自由表面的联合影响以及停滞点的出现来阐明这一主题。利用欧拉方程框架，我们采用了保角映射和伪谱数值方法。我们的研究结果表明，增加电场强度可以消除停滞点，并使波形更加平滑。这意味着水平电场是消除流体内部停滞点的一种机制。此外，我们还发现了自由表面出现三个停滞点的情况--这在纯重力旋转波中是不可能出现的。

引用次数: 0

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