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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。

And the solutions of the three problems above are discussed:The solution to the simulcast interfering which is caused by the simulcast delay spread and the zero-beating is given in chapter four.Based on the well understanding of the principle of MS-I/H/0 in IPNP, the examples are given in chapter five on how to solve the problem of communication interruption between paging zones.Through the analyse of signal switching between Chengdu and Deyang, the synchronization error between FLEX frames, and the bug in the multi-frequency roaming principle are pointed out. And solutions are also recommended.

通过以上分析，文章探讨了对上述三个问题的解决：·对同播干扰问题，分别分析了时延差和零拍频所造成同播干扰的客观存在，探讨了系统设计和网络优化的基本方法；·对IPNP联网障碍，提出了在掌握IPNP对各PNCC作为输入局／归属局╱输出局的灵活定义、以及相关参数配置原理的基础上，分析联网障碍的思路；·对信号切换障碍，以成都和德阳两地的局部广域覆盖为例，分析了FLEX帧失步和FLEX多频漫游原理设计缺陷的客观存在，并探讨了相关的解决方法和建议。

A necessary and sufficient coindition for the existence of positive solutions of a class of singular boundary value problems of higher order differential equations is given by means of the method of lower and upper solutions with the maximum principle.

摘要利用上下解方法和极大植原理给出了一类高阶微分方程的奇异边值问题正解存在的充分必要条件。

In this dissertation, many works have been done on the basis of the summarization of the merits of all kinds of meshless methods after a large number of relevant references are read and studied. The basic ideas, principles of meshless methods and their development in the recent years are introduced synoptically. Applications of Element-free Galerkin method in elastic foundation plate are studied deeply and some useful conclusions are obtained as follows:(1) Comparisons between numerical solutions and analytical solutions for several different styles of weight functions, including Gaussian weight function, spline weight function and singular weight function etc, are performed. The results show that Gaussian weight function is the best one.(2) Ranges of relevant parameters for Gaussian weight function are given.(3) Influences of nodal distribution schemes and the number of Gaussian integrated dots on computational results are discussed.

在本文中，作者在认真阅读和研究所搜集到的大量参考文献、综合各种无网格法优点的基础上，首先，对无网格法的基本思想、基本原理、发展现状作了概括性的介绍；其次，对无单元Galerkin法在弹性地基板计算中的应用进行了较为深入的探讨：(1)分别对高斯型、样条型、奇异型等不同形式的权函数进行比较分析，数值计算结果与级数解析解的比较表明，高斯型权函数效果较好：(2)对高斯型权函数进行参数研究，得到地基板计算中相关参数的选取范围；(3)对不同节点分布方案和不同高斯积分对计算结果的影响等作了有益的讨论。

To a general KdV equation with singular curves on phase plane, we explain the reason why these non-smooth traveling wave solutions arise.Based on the bifurcation analysis, all possible traveling wave solutions have been known qualitatively.

论文的第三章考虑奇异性对非线性波动方程解的结构的影响，针对相空间上出现奇异线的广义KdV方程，详细讨论了奇异线的存在对解的结构的影响，分析系统中非光滑行波解产生的原因。

And the envelope solitary wave solutions and envelope sinusoidal wave solutions have been obtained.

得到了该方程的包络孤立波解和包络正弦波解。

The envelope solitary wave solutions and envelope sinusoidal wave solutions of DNLS equation are obtained.

得到了DNLS方程的包络孤立波解和包络正弦波解。

In order to determine the solution set of the equation , by the means of meet-irreducible element and irredundant finite meet-decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet-decomposition, and then consider the relation between the equation and the equation , based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix B has an irredundant finite meet-decomposition and so determine its solution set completely.

为了确定方程的解集，本文利用交既约元与不可缩短的有限交分解等工具，同样地先求出简单形式的型矩阵方程的所有极大解，然后讨论方程与方程之间的关系，在此基础上，在B的每个元素均有不可缩短的有限交分解的情况下，求出了方程的所有极大解，从而完全确定了方程的解集。

To verify part solutions, I needed the solutions and couldn't find a solver at that time.

为了验证部分解决方法，我需要的解决方案，但没有找到当时一解算器。

In Chapter 4,we prove the existence of global weak solutions to the compressible NSP equations with density-dependent viscosity coefficients when the initial data are large and spherically symmetric by constructing suitable aproximate solutions.

在第四章里，对于粘性系数依赖于密度的等熵可压缩NSP方程，在R~3中包含球心的球状区域内，我们得到了大始值的，球对称弱解的整体存在性。

Continuously improve the production mechanism, to provide customers with better quality products and services.

不断的完善生产机制，给客户提供更优质的产品及服务。

B:Yes, he was the very prize-winner in the court tennis ten years ago?

是的，他是十年前的世界网球冠军。