查询词典 solitary wave

The auxiliary equation is directly applied to solve the (2+1)-dimensional dispersive long wave equations and the solitary wave solutions and triangular periodic wave solutions are obtained.

利用该辅助方程直接求解了(2+1)维色散长波方程，结果获得了一些孤立波解和周期解，其中包括一些新解。

The many exact solutions, such as, trigonometric function, solitary pattern solutions, solitary wave solutions, Jacobi and Weierstrass elliptic function solutions are given by the auxiliary equation method.

近来，随着计算机技术的发展，关于孤立波的研究越来越多的依赖于计算机软件的应用，随之产生了一系列求解非线性波动方程的新方法，并且这些方法逐渐的被应用到离散的非线性微分—差分系统中来研究离散系统的孤立波问题。

The paper presents a linear transient solution for the solitary wave generated by a piston-type paddle in a finite flume based on the boundary condition derived by Dean and Dalrymple (1991). The wavemaker problem is simplified by decomposing the wave potential into two parts. One is the evanescent wave and the other is progressive wave. The possible solution for the evanescent wave is expressed in form of the Fourier series.

本文根据Dean与Dalrymple（1991）描述造波水槽内部之线性边界条件，将水槽内部之流速势分为振荡波与前进波以简化问题，再以Fourier级数展开，可将问题化为二非齐次常微分方程式，在给定造波初始条件的情况下即可解析有限长度造波水槽自静止开始造波一段时间后停止之线性暂态解。

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。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

Nonlinear wave equation; nonlinear intensity; solitary wave solution; nonlinear differential-difference system; compacton; peakon; noncontinuous solitary solution; bifurcation

非线性波动方程；非线性强度；奇异孤立波；非线性微分—差分系统；紧孤立了；尖峰孤立子；不连续孤立波；分岔

By using the theory of bifurcations of dynamical systems to the generalization form of the modified KdV equation, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained.

本利用动力系统的分支理论来研究一类广义MKdV方程的行波解，得出了孤立波、扭子、反扭子和不可数无穷多个光滑和非光滑周期解的存在性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失