孤立子

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

In the bounded linear operator approximation theory of Hilbert Space,the isolate point of operator essential spectrum is always a problem. In this paper,a general method to treat this problem is given.

孙辉在Hilbert空间线性算子逼近论中，算子本质谱的孤立点通常是处理一些问题的主要障碍之一，本文给出处理算子本质谱的孤立点的一般方法。

Then(1) There exist controvertible normal operators E, F, such thatand 0 is an isolated point in is an isolated point in ,(2) There exist a series of operator An, such that

存在可交换得正常算子El，使得 T＝AO－A＝EF＝FE 且 0是。p）的孤立卢、eso是口p）的孤立。点，＊存在一列算子＊＊使得 lAnAll－ 0，n、co

In Chapter 7, we prove the resolvent operator of compound KDV equation is computable via the operator method, contraction mapping principle and TTE theory.

第五章应用Backlund变换得到了变系数组合KdV-Burgers方程的N-类孤子解；第六章应用F展开法及其扩展形式得到了变系数组合KdV方程和(n+1)维Sine-Gordon方程的孤立波解；第七章运用算子方法、压缩映象原理和TTE理论，证明了组合KdV方程的解算子是可计算的；最后对全文进行了总结，并对未来的研究方向作了展望。

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。

By using the pseudo 3-D fKdV equation and division of four regions, theoretical mean wave resistance s and time change rates of the regional mean energy of the precursor soliton generation in a straight channel with arbitrary section are given theoretically.

利用准三维的fKdV方程和四区间划分法，理论给出了任意截面的直渠道中先锋孤立子生成的理论平均波阻和区间平均能量的时间变化率。

The soliton hierarchies associated with the modified second order polynomialeigenvalue problems can be factorized into the commuting x- and 〓-constrainedflows, the r-matrices and classical Poisson structures for the x- and 〓-constrained flows are constructed.

与修正的二阶多项式特征值问题相联系的孤立子方程族可以被分解为相互交换的x-和〓-约束系统，本文求出了约束系统的r-矩阵和经典Poisson结构。

Chapter one involves a survey of the fundamental knowledge and achievement obtained by foregoers on the subjects for the purpose of the later parts in this dissertation, including the introduction of the history and development of mathematics mechanization, brief review of the history and status in quo of the fractional calculus and soliton theory.

第一章介绍了论文的基础知识以及前人工作的成果：包括介绍数学机械化的思想与应用的情况；回顾分数微积分的历史和所应用的领域；简单介绍孤立子研究的历史、发展与成果。

In anomalous dispersion of monomode optical fiber, an optical soliton is evolved from an optical pulse in the fiber when the nonlinearity is balanced by dispersion.

摘要在单模光纤异常色散区，当非线性与色散平衡时，初始注入的光脉冲演化形成光孤立子。

This approach can be applied to all other (1+1)-dimensional solitonhierarchies with self-consistent sources.

这一方法可以应用于求解其它带附加项的1+1维孤立子方程族。

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