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In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

In this paper,the asymptotic property for two kinds of ecological systems and oscillation for solutions of a neutral differential equations is studied by employing differential inequalities and using eigenvalue analysis,iterative algorithm,induction and comparison theorem etc.Here, the system\'s asymptotic property includes the uniform persistence,the global attractability of the solutions,the asmptotic stability of the solutions and the oscillation of solutions.

本文利用微分不等式、特征根分析法、迭代法、归纳法及比较原理等方法和理论，研究了两类生态模型解的渐近性和一类脉冲中立型微分方程解的振动性，其中包括模型的一致持久生存性，正平衡态的全局吸引性、局部与全局渐近稳定性以及解的振动性。

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 many exact solutions and compact-like solutions uch as,trigonometric function,solitary pattern solutions, solitary wave solutions are given by the auxiliary equation method.

在第六章，我们将指数函数法(Exp-function method)应用到一类变系数非线性波方程中，借助计算软件Maple得到了组合变系数KdV-mKdV方程的广义孤立波解。

The reliability theory is combined with the fuzzy optimization technique, the theories and methods on the symmetrical fuzzy reliability optimization design, the asymmetric fuzzy reliability optimization design and the multi-objective fuzzy reliability optimization design are presented respectively, and then the correspondence direct model solutions, the iterative solutions, the corrected algorithm for iteration method, the level cuts solutions and the searching solutions with limited boundary for the asymmetric fuzzy reliability design are presented respectively.

将可靠性理论与模糊优化技术有机地结合起来，提出了结构对称模糊可靠性优化设计、非对称模糊可靠性优化设计和多目标模糊可靠性优化设计理论与方法，并分别给出了模型的直接解法、迭代解法、迭代求解的改进算法和非对称模糊可靠性优化设计模型的水平截集法和限界搜索法。

In chapter 3,we study the Zakharov-Kuznetsov-Modified Equal-Width equation by employing the extended Jacobi elliptic function expansion method and obtain some new solutions of Jacobi elliptic function type of the ZK-MEW equation.;Secondly,using sn-cn method,we study K(m,n,1) equation and obtained some new exact solutions when k=s=3,especially obtained abundand solitary solutions and trigonometric function solutions when m→0 and m→1;In chapter 4,Painleve singular analysis was applied to nonlinear PDE with variable coefficients.

第四章将Painleve奇性分析方法应用到带阻尼项的变系数Burgers方程中，并得到了该类Burgers方程具有Painleve性质的条件，给出了该类Burgers方程的Backlund变换，用所得Backlund变换得到了若干精确孤立波解，包括奇异孤立波解，这些解不等同于行波型孤立波解；用齐次平衡法得到了对数型DBM方程的Backlund变换，并获得了DBM方程的各种孤立波解，包括尖峰孤立波解和奇异尖峰孤立波解。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

By means of the undetermined coefficient method ,which is submitted in reference for solving nonlinear wave equations for their peaked soliton solutions ,three kinds of peaked soliton solutions are obtained for two important nonlinear wave equations— Korteweg-de Vries equation and Benjamin-Bona-Mahonyequation,respectively. One kind of peaked compacton solution ,which has the characteristics of both peaked soliton solution and compacton solution ,is obtained for above two equations with the aid of transformation relation between triangle function and hyperbolic function,. By use of above solutions, two kinds of periodic peaked traveling wave solutions are constructed.

摘 要：利用文献中提出的求非线性波方程尖峰孤子解的方法，分别求解了两个重要的非线性波方程—Korteweg-de Vries 方程和Benjamin-Bona-Mahony BBM）方程，得到了3类尖峰孤子解；借助双曲函数与三角函数间的变换关系得到了1类尖峰紧孤子解，该型解兼有尖峰孤子解和紧孤子解的特点；在上述结果的基础上构造了2个周期性的尖峰行波解。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

Ion exchanage materials are also used to purify the chlorous acid and chlorine dioxide solutions, without causing degradation of said solutions, to exchange undesirable ions in the chlorous acid and chlorine dioxide solutions with desirable ions, such as stabilizing ions, and to adjust the pH of chlorous acid and chlorine dioxide solutions.

所述离子交换材料也可以用于纯化亚氯酸和二氧化氯溶液，从而在亚氯酸和二氧化氯溶液中用想要的离子如稳定离子交换不想要的离子，并调节亚氯酸和二氧化氯溶液的pH值，而不造成所述溶液的质量降低。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。