Influence of nonlinearly induced diffraction on spatial solitary waves

Spatial solitary waves carried by a TE mode in planar optical waveguides with Kerr-type of nonlinearity are investigated based on a modified nonlinear (1 + 1) Schrödinger equation. Looking for effects instigated by the spatial inhomogeneity of the nonlinear polarization, the nonzero divE-term is taken into account in the nonlinear guided wave equation together with the nonparaxial approach and vector model. It is shown that, at self-focusing of beams in a (1 + 1) geometry, the effect coming out from the divergence term predominates over modifications related to the nonparaxial vector model. This term is interpreted as nonlinearly induced diffraction which plays the role of an effective saturation. Analytical solutions supported by numerical results are found.     

Electromagnetically induced transparency in a non-uniform plasma

Electromagnetically induced transparency in a non-uniform plasma is investigated. We discuss the possible frequency ranges in which a weak beam below cutoff can propagate transparently in this plasma with the presence of a strong high frequency field. We also analyze the effect of driving intensity on the frequency range of the probe. Received 3 March 2000 and Received in final form 21 April 2000     

On the linear stability of simple and semi-simple periodic waves for a system of cubic Klein–Gordon equations

We study the linear stability of traveling wave solutions for the nonlinear wave equation and coupled nonlinear wave equations. It is shown that periodic waves of the dnoidal type are spectrally unstable with respect to co-periodic perturbations. Our arguments rely on a careful spectral analysis of various self-adjoint operators, both scalar and matrix and on instability index count theory for Hamiltonian systems.     

Traveling Waves in Degenerate Diffusion Equations

In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited diffusion equations, delayed degenerate diffusion equations, and other strong degenerate diffusion equations.     

Transition,coexistence, and interaction of vector localized waves arising from higher-order effects

We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system.     

水下目标几何声散射回波在分数阶傅里叶变换域中的特性

水下目标散射回波在时域、频域混叠在一起, 而且受声波入射角度的影响严重, 在不同的入射角度下表现出很大的差异, 需要建立全方位入射角度下回波分量的理论分析模型. 本文推导了目标几何声散射分量在分数阶傅里叶变换域中随入射角度变化的解析表达式; 确定了目标几何声散射回波分量在最佳分数阶傅里叶变换域中的全方位模型, 从理论上证明了目标回波的几何特征形式; 给出了离散分数阶傅里叶变换对声散射分量的分辨能力和计算精度与发射信号带宽和观测时间之间的关系. 实验数据处理表明, 建立的分数阶傅里叶变换域的全方位模型与目标几何特征是一致的, 对未知入射角度下的目标识别提供了理论依据.     

Relativistic degenerate effects of electrons and positrons on modulational instability of quantum ion acoustic waves in dense plasmas with two polarity ions

The nonlinear propagation of quantum ion acoustic wave(QIAW) is investigated in a four-component plasma composed of warm classical positive ions and negative ions,as well as inertialess relativistically degenerate electrons and positrons.A nonlinear Schrodinger equation is derived by using the reductive perturbation method,which governs the dynamics of QIAW packets.The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf.The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit,the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively,and on the relativistically degenerate effect as well.     

层结流体中在热外源和β效应地形效应作用下的非线性Rossby孤立波和非齐次Schrödinger方程

在层结流体中, 从带有地形、热外源耗散的下边界条件以及带有热外源的准地转位涡方程开始, 使用小参数展开方法和多尺度时空伸长变换推导出了具有热外源、β效应和地形效应的强迫Rossby孤立波方程, 得到孤立Rossby振幅满足的带有地形与热外源的非齐次非线性的Schrödinger方程. 通过分析Rossby孤立波振幅的变化, 指出了热外源、β效应和地形效应都是诱导Rossby孤立波产生的重要因素, 给出了切变基本流下地形、热外源和层结流体中Rossby的相互作用.     

Particle paths in Stokes’ edge wave

We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation which decreases with depth and distance from the shoreline. We discuss the application of this rotated coordinate frame to higher mode (Ursell) and weakly nonlinear (Whitham) edge waves, and show that the weakly nonlinear case is identical to that for two-dimensional deep-water Stokes waves.     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.