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In this paper, the method of wave field extrapolation and decomposition of seismic compound wave in viscoeleastic medium is presented, based on wave equation.

从粘弹性波动方程出发，建立了一种地震散射波场纵横向高分辨波场外推方法。

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current.

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。

A new prestack depth migration method that is based on wave field continuation has been developed by combining physical model of plane wave synthesizing with Fourier finite difference operator for wave field continuation.

本文将平面波合成的物理模型与傅里叶有限差分波场延拓算子相结合，提出了一种新的基于波场延拓的叠前深度偏移方法。

To take control of the propagation direction over the electromagnetic wave, or even over the propagation direction of wave, including light-wave, is a promising research target.

控制电磁波的传播方向，甚至控制包括光波在内的波的传播方向，是一个充满前景的研究目标。

On this basis, we further analyze the situation of backward wave in anisotropic metamaterials with different dispersion relations, and the angle between wave vector and Poynting vector, and the general conclusion of backward wave propagation are obtained.

在此基础上，进一步分析了几种不同色散曲线关系的各向异性超常材料中倒退波的产生情况，获得了电磁波波矢和坡印亭矢量夹角的具体表达式和倒退波传播的一般性结论。

PartⅡ,Applying the developed and extended direct algebraic methods that presented in recent years and based on the 2+1 dimensional variable separation solutions,abundant Jacobi elliptic function doubly periodic waves and periodic propagating wave patterns for many 2+1 dimensional nonlinear wave models are obtained,and in long wave limit solitary waves are derived as well.

第二部分，本文拓展和推广(来源：a2AB7aC论文网www.abclunwen.com)了新近发展的几种典型的直接代数方法和基于分离变量解的间接方法，获得多个2+1维非线性波动模型丰富的雅克比椭圆函数双周期波解和周期传播波模式，并得到长波极限情形下存在的非线性孤立波。

Correlation analysis of the two lists of the probe signals are done by using the statistic method. Void wave instantaneous velocity probability distribution graphs and the graphs of a relation between void wave average velocities and fluxes are obtained. The comparison between the fitting lines and the theoretical formulation of void wave velocity is drap.

通过统计的方法对两列探针获得的局部瞬时空隙率信号进行相关性处理，得到不同流量和不同外加扰动下空隙率波瞬时波速概率分布图及空隙率波平均波速和流体流速关系图，并对空隙率波平均波速拟合直线和空隙率波波速理论公式进行比较。

Nonlinear flexural wave equation is solved by the Jacobi elliptic function expansion method. Two kinds of exact periodic solutions of the nonlinear equations are obtained, that is, the shock wave solution and the solitary wave solution. The necessary condition for existence of exact periodic solutions, shock solution and solitary solution is discussed, which is consistent with the qualitative analysis.

利用Jacobi椭圆函数展开法，对该非线性方程进行求解，得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解，讨论了这些解存在的必要条件，这与定性分析的结果完全相同。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

This paper proposes an equivalent second order elastic wave equation to solve the problem of being unable to completely separate the coupled P and S wave by full elastic wave equation.

给出了一种等价的二阶弹性波动方程，以解决弹性波场中完全弹性波动方程不能完全分离耦合的纵、横波波场问题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。