孤波

Some new exact solitary wave solutions of an auxiliary ordinary differential equation were obtained by the trial method.

通过试探方法得到辅助常微分方程的一些新的孤波解。

By utilizing the auxiliary ordinary differential equation and its solutions, the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method, and abundant new exact solitary wave solutions were obtained under certain conditions.

利用该方程及其解，采用改进的tanh函数展开法研究了第1类和第2类变系数KdV方程，获得了在一定条件下的若干新精确孤波解。

Combined KdV equation; Generalized KdV equation; Reduction-order method; Auxiliary differential equation technique; Solitarywave solutions; Periodic solutions; Solitons; Algebraic travelling wave solutions; Physical structures

基础科学，数学，数学分析KdV-mKdV方程；广义KdV方程；降阶法；辅助微分方程；孤波解；周期解；孤子解；代数行波解；物理结构

Some of them such as the South China Jiao Ao down, and some belly landing and may Chihuahua; some家财万贯, wealthy, and some to both color and poor milk no match; some pie incarnation, and some variation of the full moon, wet socks off some legs, some chest hidden devices; some sister-pronged battle, his family south, and some enter孤狼alone, all the way north; some wearing X cards natural mother, some of the blame if the animal food force female;满纸more that directory, empty cans everywhere ...... the face of the enemy's getting pounded and wave after wave of counterfeit tickets and ANTI offensive, in the pre-war Kyoto, has already fallen too much on the elite.

他们有的傲娇如华南虎下山，有的腹黑似吉娃娃落地；有的家财万贯、富可敌国，有的才色兼备、贫乳难敌；有的馅饼化身，有的满月变异，有的脱袜湿腿，有的暗藏胸器；有的姐妹齐上阵，举家朝南，有的孤狼独闯关，一路向北；有的是头戴X卡的天然娘，有的是食量如牛的怪力女；更有那目录满纸，空罐遍地……面对敌人的围追堵截和一波又一波伪票与ANTI的攻势，在预选战中，京都就已经倒下了太多的精英。

In a word, the solitary evolution and propagation of the matching Gauss beam is quite close to those of the DHSP in the dissipative system.

总之，在耗散系统中，匹配的高斯孤波的动态演化特性与耗散全息屏蔽光伏明孤波的演化特性是相符合的。

The dependence of wave velocity on Reynolds number is analyzed, and the results are in agreement with the previous theoretical and experimental results.

计算给出了孤波波速与雷诺数之间的关系曲线，该曲线与文献中的理论和实验结果相吻合。

This dissertation studies some topics in soliton and integrable system,which mainly include as follows:exact solutions especially travelling wave solu-tions and solitary wave solutions,Painlevēproperty,transformation,similarity reduction,symmetries and their Lie algebra structure,generation ofsoliton hierarchy and their zero curvature representation,Hamiltonian struc-ture,Lax or Liouville integrability,nonlinearization of Lax pairs,applications ofWu's method and symbolic computation.

本文研究内容涉及到孤立子和可积系统的多个方面：精确解特别是行波解和孤波解，Painlevē性质、变换、相似约化、对称及其Lie代数结构、孤子族的生成及其零曲率表示，Hamilton结构，Lax和Liouville可积性、Lax组的非线性化以及吴方法和符号计算在上述研究中的应用。

Introducing single valued and multivalued functions properly in the 2+1 dimensional variable separation solutions,we derive various semifolded solitary waves such as bell-like semifolded soliton,compaction-like semifolded soliton and peakon-like semifolded solitons,et al.

在2+1维分离变量解中引入多值函数和不同单值函数，得到了多种半折叠孤波激发，如钟状半折叠圈孤子、Compacton半折叠圈孤子、Peakon半折叠圈孤子等。

Both the rarefactive and compressive waves can be determined by plasma parameters including the temperatures of dust fluid, ion and electron, as well as the non-thermal ions, and the number densities of dust particle , ion and election, etc.

而稀疏孤波和压缩孤波的存在则完全取决于尘埃等离子体参数，如：尘埃流体、离子和电子的温度，非热离子的快离子数以及尘埃颗粒、离子和电子的数密度等。

The results shows that: as the fast ions numberα=0, ie., the ions number density reduces to the Boltzmann ion distribution, the solitary waves are all rarefactive, which are in good agreement with Ref. [81]. as the fast ions increases, the compressive waves can also exist in some special regions.

结果表明，当快离子数为零时(α=0)，即离子分布退化为玻耳兹曼分布时，该系统只允许稀疏形孤波存在，这与文献[81]的结论相一致；而随着快离子数的增加(α≠0)，在某些特定的区域，还会出现压缩形孤波。

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