Bifurcations and new exact travelling wave solutions for the bidirectional wave equations

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional wave equations. The results presented in this paper improve the related previous studies.     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.     

Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.     

等离子体中电磁波传输特性理论与实验研究

本文对35 GHz和96 GHz电磁波在等离子体中的传输特性进行了理论与实验研究, 得到了电磁波衰减随等离子体密度、碰撞频率和电磁波频率的变化规律. 等离子体密度增加一个数量级时, 电磁波衰减增加一个数量级; 随着等离子体碰撞频率的增加, 电磁波衰减先增加后减小; 随着电磁波频率的增加, 衰减下降. 以激波管为实验平台进行了电磁波在等离子体中传输特性的实验研究, 实验结果和理论结果吻合较好. 理论和实验结果均表明, 提高电磁波频率是解决黑障问题的有效途径.     

WAVENUMBER PREDICTION OF WAVES IN BURIED PIPES FOR WATER LEAK DETECTION

Water leaks are a topic of great concern in Britain and many other countries, because of decreasing water supplies and the deterioration of old pipework. Correlation techniques are widely used in leak detection, but for these to be effective, the propagation wavespeeds and wave attenuation must be known. Relatively predictable for metal pipes, these are largely unknown for the newer plastic pipes, being highly dependent on the pipe wall properties and the surrounding medium. In this paper, pipe equations for n=0 axisymmetric wave motion are derived for a fluid-filled pipe, surrounded by an infinite elastic medium which can support both longitudinal and shear waves. These equations are solved for two wave types,s =1,2, which correspond to a fluid dominated wave and an axial shell wave, and expressions for a complex wavenumber for each wave are given.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

Transmission scatter cross sections across two-dimensional random rough surfaces – full wave solutions and comparison with numerical results

Abstract

In this paper, the full wave expressions for the bistatic transmission scattering cross sections across two-dimensional random rough surfaces are obtained. The full wave analysis accounts for the surface height/slope correlations. Analytical and numerical comparisons of the full wave solutions with the small perturbation and physical optics solutions are made for isotropic random rough surfaces. The full wave results are also compared with the numerical results based on Monte Carlo simulations of one-dimensional random rough surfaces. Detailed consideration is given to illustrating the relationship between these full wave solutions and the original full wave solutions including the impact of accounting for the height/slope correlations in this analysis.     

等离子体波在喇曼自由电子激光中的作用

本文用参量放大器模型,分析了喇曼型自由电子激光中等离子体波的作用。结果表明,在忽略电子束初始横向速度的情况下,慢等离子体波与散射波耦合的必要条件为k_wv₂₀>ω_c,即电子的平衡态运动应处于第一组轨道。文中还求出散射波的色散特性和增益公式,以及散射波与等离子体波的相位匹配关系。 关键词：     

Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters

Bessel solitary wave solutions to a two-dimensional strongly nonlocal nonlinear Schrödinger equation with distributed coefficients are obtained. Bessel solitary wave solutions have unique characteristics compared with Gaussian solitary wave solutions, Laguerre-Gaussian solitary wave solutions, and Hermite-Gaussian solitary wave solutions. The generalized two-dimensional nonlocal nonlinear Schrödinger equation with distributed coefficients is investigated for the first time to our knowledge.     

Shock Wave Propagation in Gases and Low Temperature Plasma Under Subatmospheric Pressure

Results of investigation of the shock wave dynamics under subatmospheric pressure in neutral gases and weakly ionized low temperature plasma are presented. The characteristics of spherical and plane configuration shock wave excitation and propagation in gases in the pressure region 1 Torr < p <100 Torr are studied. The same is done for the plane configuration shock wave in weakly ionized plasma in the pressure region 1 Torr < p <10 Torr. It is shown that when p = 3 Torr it is still possible to fix successfully the shock wave appearance and propagation in various neutral gases. The pressure dependence of the shock wave propagation velocity and amplitude is determined experimentally. It is shown that when the pressure decreases the shock wave amplitude decrease and the increase of the Mach number take place. In the case of plane shock wave Mach number reaches the value M = 5.2 under the pressure p = 3 Torr. As for shock wave propagation in low temperature plasma, our experiments showed a significant decrease of wave amplitude and simultaneous increase of its velocities up to 35 wave velocity is related to the heating of neutral gases in plasma.     

Evanescent Plane Waves in Multilayer Structures

We have considered evanescent plane waves in structures with a layer of a substance with ε, μ < 0 and with a layer of a well-reflecting metal, ε < 0, μ ≥ 1. Waves with increased amplitude as compared with the initial wave have been found to occur, due to which evanescent waves with wave number as in the initial wave but with increased amplitude arise behind these layers. A composite material with ε, μ < 0 at optical frequencies are proposed. Surface waves on a metal layer are considered in detail. It is shown that surface waves with a sufficiently arbitrary wave number can be excited. It is also shown that, on very thin layers, surface waves with wave number exceeding ten times that of a homogeneous plane wave in vacuum can be excited. Propagation losses are calculated. For a silver layer, the wave path can be from 30 up to 100 wavelengths. Practical use in developing techniques for optical transformations of short-wave surface waves in 2D space, similar to those in 3D space, are pointed out.     

Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves

The wave equation for a scalar field ? and vector potentialA* are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave, is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the other shows a transient character. There is no interaction when the waves are along the same direction.     

W波段回旋行波管放大器的模拟与设计

回旋行波管放大器是高功率毫米波雷达发射系统最重要的候选者.通过对回旋行波管放大器中的绝对不稳定性、回旋返波振荡以及电子注-波互作用的研究，讨论了回旋行波管的稳定性、寄生模式的抑制和工作参数的优化等问题，给出了W波段TE₀₁模回旋行波管放大器的模拟设计结果.PIC粒子模拟结果表明，在电子注电压100kV、电流10A、工作磁场3.52T时，94GHz的基波回旋行波管放大器可获得大于250kW的输出功率、40dB的增益、大于25％的效率和约5％的带宽. 关键词： W波段 回旋行波管放大器 模拟 设计     

THE RELATIVISTIC DEUTERON WAVE FUNCTION

Starting from the Bethe-Slapeter equation, the coupled equations for the bound states of the deuteron may be reduced to the ordinary three dimensional ones and the number of the components of the wave function is decreased by using the approxima-tion of the instantaneous interaction in the center of mass system. The wave functions of the deuteron are expanded in terms of the spherical and the vector spherical har-monics and the radial coupling integral equations are obtained. Some properties of the deuteron wave functions are discussed also. Qualitative estimations indicate that the relative ratio of the probability of P wave to that of S wave is about the order of(1/2)|(p/m)|²     

fN组态波函数的Young盘形式

本文给出用Young盘表达f^N组态谱项波函数的系统方法,特别是表达简并谱项波函数的方法,使得谱项的波函数和Racah群链的态分类一致。 关键词：     

Shock wave propagation in gases under subatmospheric pressure

In the present paper the results of the experiments on the shock wave dynamics under subatmospheric pressure in neutral gases are presented. The characteristics of spherical and plane configuration shock wave excitation and propagation are studied in the pressure region 1 torr<p<760 torr. It is shown that whenp=3 torr it is still possible to fix successfully the shock wave appearance and propagation in various neutral gases. The pressure dependence of the shock wave propagation velocity and amplitude is determined experimentally. It is shown that when the pressure decreases the shock wave amplitude decreases and an increase of the Mach number takes place. In the case of plane shock wave the Mach number reaches the valueM=5.2 under the pressurep=3 torr.     

Knotted Wave Dislocation with the Hopf Invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the φmapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations. PACS 02.10.Kn, 02.40.-k, 11.15.-q     

Nonlinear evolution of a three-dimensional transverse wave packet in a hot plasma including the effect of its interaction with an ion-acoustic wave

By a perturbation method two coupled nonlinear partial differential equations are obtained for the nonlinear evolution of a three dimensional transverse wave packet in a hot plasma including the effect of its interaction with a long wavelength ion-acoustic wave. From these two equations a nonlinear dispersion relation is obtained, from which the instability condition of a uniform transverse wave train including the effect of its interaction, both at resonance and at nonresonance with a long wavelength ion-acoustic wave, are deduced. Resonance occurs when the component of group velocity of the longitudinal wave along the direction of propagation of the ion-acoustic wave is equal to the phase velocity of the wave. Assuming the usual type of dependence of amplitude on space and time the coupled equations are transformed into two other coupled equations, which reduced to a single nonliear Schrödingsr equation when three dimensionality is disregarded. It is found that these three transformed equations cannot give instability condition at resonance.On leave fromThe Department of Mathematics, University of Kalyani, West Bengal, India.     

托卡马克中快波电流驱动下全波方程的数值求解

用全波方法研究环形对称托卡马克等离子体中离子回旋频率范围内(ICRF)的快波电流驱动(FWCD)问题,考虑有限拉莫尔半径(FLR)效应和平行色散,建立全波计算的物理模型—全波方程,通过对全波方程的数值求解得到快波在等离子体中激发的电场强度分布.结果表明:快波可以传播到高温高密度等离子体的中心;快波在磁轴附近发生了模式转换;快波可以驱动中心的等离子体电流以改善等离子体的平衡位型;平行电场比垂直电场小三个数量级,通过垂直方向的回旋共振和平行方向的穿越期磁泵效应达到驱动电流的目的.     

Partial Wave Crossing Relations for Meson-Baryon Scattering

Three different types of relations for meson-baryon partial wave amplitudes following from the s ↔ u crossing symmetry of the invariant amplitudes are investigated: i) the partial wave crossing relations directly derived from the s ↔ u crossing symmetry and the partial wave projection, ii) the partial wave crossing relations following from a combined use of s ↔ u crossing symmetry and analyticity, and iii) the crossing sum rules, which are a direct consequence of the s ↔ u crossing symmetry. The kernels entering the crossing relations i) and ii) are given in an analytic form, valid for arbitrary angular momentum. Their properties are studied in detail. By means of the partial wave crossing relations ii) it is demonstrated that u-channel exchange of a resonance leads to a resonance-like behaviour of the partial wave amplitudes on the crossed physical cut. This phenomenon is described in terms of “pseudoresonances”. Finally the crossing sum rules iii) and their practical use are thoroughly discussed, and they are compared with the partial wave crossing relations i) and ii). Special attention is paid to the crossing symmetry constraints on the S-wave amplitudes. As a result of these investigations we present a crossing symmetric ansatz for these amplitudes which gives a more reliable parametrization than the usual effective range approximation.