Chapter one studied the finite difference methods of a class of high-order wave equations?
第一章研究了一类高阶波动方程的有限差分法。
By using a mapping method, we obtain exact solutions of the (2 + 1) dimensional long wave equations.
运用数学中的映射方法分析论证，获得了(2 +1)维长波方程组的精确解。
The SBS coupled wave equations are solved numerically and laser induced stress is obtained spatially.
数值求解了SBS耦合波方程组，得到了SBS诱导应力的时空分布。
The results show the method is simple and effective and can be applied to other nonlinear wave equations.
结果表明该方法简单有效，并且可以应用到其它的非线性波动方程。
A general solution of multiple scattered waves in solids based on wave equations of heat conduction is given.
基于热传导波动模型给出了物体中热波多重散射问题的一般解。
Auxiliary equation method is extended and applied to 2-dimensional generalized dispersive long wave equations.
用辅助方程法构建二维广义色散长波方程的精确解。
Lattice systems and nonlinear wave equations are two kinds of very important infinite dimensional dynamical systems.
格点系统与非线性波动方程是两类很重要的无穷维系统。
The solving of wave equations and tortuous ray method are fundamental methods of analysing plane optical waveguiding.
曲折光线法和解波动方程是分析平面光波导的基本方法。
The periodic initial value problem of a class of generalized symmetric regularized long wave equations is considered.
考虑了一类广义的对称正则长波方程的周期初值问题。
We consider the initial boundary value problem for a class of nonlinear degenerate wave equations in a bounded domain.
考虑了有界区域上一类非线性退化波动方程的初边值问题。
This method used in the paper can be also be applied to other nonlinear wave equations with higher-order nonlinear terms.
这种方法同样也适用于求解具有更高次非线性项的其他非线性波方程。
The relation between linewidth broadening factor and semiconductor's linewidth can be obtained by utilizing wave equations.
利用波动方程，得到了线宽增长因子同光源线宽的关系；
Under appropriate conditions, the approximate solutions for two nonlinear wave equations are obtained simply and conveniently.
在适当的条件下，较简捷地得出了这两类非线性波方程的近似解。
The existence and uniqueness of global solution for the nonlinear wave equations with acoustic boundary conditions are obtained.
研究具有声学边界条件的非线性波动方程初边值问题，得到整体强解的存在惟一性。
More explicit travelling wave solutions can be obtained by using this method to solve other nonlinear travelling wave equations.
将该方法应用于其它非线性波方程(组)中，可获得更多的显式行波解。
The characteristic method is applied and the weak discontinuous solutions of homogeneous quasilinear wave equations are discussed.
主要分析一维拟线性波方程的解的间断性。
The long time behavior of solutions of the generalized symmetric regularized long wave equations with dissipation term is considered.
该文考虑了带有耗散项的广义对称正则长波方程解的长时间性态。
Modified coupled-wave equations are used to calculate the effect of grating shape on coupling coefficient of the second-order gratings.
利用改进的耦合波理论计算了具体器件结构中光栅形貌对二级光栅耦合系数的影响。
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied.
证明了具周期系数的边值问题正时间周期解的存在性以及对应初边值问题解的渐近性。
Some new exact elliptic periodic solutions of the dispersive long wave equations in (2 + 1) dimensions are obtained by using the method.
在此基础上，得到2 +1维耗散长波方程组的椭圆周期解。
Using dyadic method, non-homogeneous wave equations of time-harmonic electromagnetic field are solved directly, several examples are calculated.
运用并矢代数方法，直接求解时谐电磁场的非齐次波动方程，并给出应用实例。
By using potential well family method, we study the invariant sets and vacuum isolating behaviour of solutions to a class of nonlinear wave equations.
应用位势井族方法，研究了一类非线性波动方程的不变集合与解的真空隔离，证明了当初始能量小于位势井深度时，此问题存在不变集合与解的真空隔离现象。
The exact solutions to dispersive long-wave equations are obtained by a polynomial expansion method based on the idea of the homogeneous balance method.
基于齐次平衡法的思想，利用多项式展开法解得了具有色散项的长波方程组的精确解。
The wave equations, modes coupled coefficient and Poynting vector have been got here. The sensing theory of tilted fiber Bragg grating is presented here.
采用耦合模理论对倾斜光纤光栅的传播特性进行分析，并推导出模式传播的波动方程、模式间的耦合系数及坡印亭矢量。
Theory of fiber optical parametric amplifiers (FOPAs) is introduced and the expression for the gain of FOPAs is deduced from the basic coupled wave equations.
介绍了光纤光学参量放大器的理论，基于耦合波方程推导出光纤光学参量放大器的增益表达式。
The bifurcation of travelling wave solutions for the generalized water wave equations are studied by using the bifurcation theory of planar dynamical systems.
应用动力系统分支理论，研究广义水波方程组行波解的分支。
In this paper, the initial-boundary value problem of a kind of nonlinear fourth-order wave equations with damping and source terms is studied on the base of Beam equation.
本文在梁方程的基础上研究了一类具有非线性阻尼项和力源项的四阶波动方程的初边值问题。
In this paper, we present a new method to solve the Cauchy's problem of the homogeneous wave equations of three dimensions, which appear comparatively simple and feasible.
本文提出了一类齐次三维波动方程柯西问题求解的新方法，该方法比一般的求解方法更简便。
In this paper, we present a new method to solve the Cauchy's problem of the homogeneous wave equations of three dimensions, which appear comparatively simple and feasible.
本文提出了一类齐次三维波动方程柯西问题求解的新方法，该方法比一般的求解方法更简便。
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