孤波

One of the single soliton solutions has the kink-antikink structure and this solution reduces to the kink-like solution and the bell-like solution under different limitation.

在不同的极限情况下，该解分别退化为mKdV方程的扭结状或钟状孤波解。

It is also found that the cross section of a Gaussian beam has the maximal influence on its solitary wave evolution.

同时发现，高斯光束的波形即光束的横截面对其孤波演化的自偏转影响最大。

Using cubic spline interpolation function, we construct a finite element model to approximate the nonlinear Schr〓dinger equation, and provide a complete discrete scheme with the conservation properties of mass and energy.

本章从应用角度出发，着重讨论孤波形式的解的计算，为此我们利用三次样条函数的插值基函数构造出非线性薛定谔方程的一个有限元离散模型，给出了具有保质量与能量守恒的全离散计算格式。

Extended elliptic function expansion method is applied to construct the explicit exact solutions of the Zakharov Equation.

将改进的Jacobi椭圆函数展开法应用到Zakharov方程，比较方便地得到新的解析周期解(包含冲击波解、孤波解和双曲函数解)。这种方法也适用于其他非线性方程或方程组

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。

The Jacobi elliptic function-like solution and trigonometric function solution of variable coefficient KP equation.

获得了变系数KP方程新的类孤波解、类Jacobi椭圆函数解和三角函数解。

Fisher Equation can be used to describe nonlinear phenomena in the problems as far as hydromechanics , plasma physics , thermonuclear reaction and the population multiplication are concerned .

方程可以用来描述流体力学，等离子体物理，热核反应和人口增殖等问题中的非线性现象，有许多文献研究它的孤波解。

Nowadays, the study of solitary waves in plasma is one of the hot topics.

等离子体中的孤波研究是目前的热门研究课题之一。

With the combined method, some new types of solutions of the (2+1)-dimensionalcubic nonlinear Schr?

其次将求非线性发展方程精确解的广义射影Riccati方程法与求对称变换群的楼直接法框结合，研究了(2+1)-维色散长波方程，得到了一些新的类孤波解。

Based on two order approximation of the variation of refraction index produced by self-action while optical pulses are traveling in Kerr-medium,the propagation equation has been solved.Furthermore,the strict analytical expressions of the amplitu

文摘：将光脉冲在克尔介质中自作用产生的折射率变化作二阶近似，求解所得到的传播方程，得到啁啾高斯脉冲幅度，脉冲宽度和周啾参数随传播距离变化的严格解析解，讨论了基模高斯脉冲孤波传播的条件。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷