孤立子

Mathematics mechanization; Symbolic computation; Exact solution; Auxiliary equation method; Soliton

基础科学，数学，数学分析数学机械化；符号计算；精确解；辅助方程法；孤立子

We also made some efforts to extend the HAM. As an example, we got the bell-like solitary wave solutions of KP equation by this approach.

同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili方程的钟形孤立子解。

In this paper,we are concentrated on the Lund-Regge equation which describes the motion of some strings.

弦运动和孤立子都是长期以来人们颇感兴趣的问题。

Nonlinear evolution equation is an important mathematical model for describing physical phenomenon and an important field in the contempary study of nonlinear physics, especially in the study of soliton theory.

非线性演化方程是描述物理现象的一类重要数学模型，也是非线性物理特别是孤立子理论最前沿的研究课题之一。

Finding the exact solution of nonlinear evolution equations is one of very important topic in soliton theory.

非线性发展方程的精确求解是孤立子理论中的一个重要研究课题。

Using the soliton theory we obtain a method to contract isometric immersions from indefinite space forms into indefinite space forms with the same index.

我们利用孤立子理论得到了构造有相同指标的不定度量空间型到不定度量空间型的等距浸入的方法。

Using the soliton theory we obtain a method to contruct isometric immersions fromindefinite space forms into indefinite space forms with the same index.

靳红 ，陈维桓我们利用孤立子理论得到了构造有相同指标的不定度量空间型到不定度量空间型的等距浸入的方法。

In chapter 4, we investigated the behavior of wave in a nonlinear monatomic chain with damping. Parameter dissipation nonlinear Schrodinger equation of lattice dynamics is first obtained. Then we discuss effect of damping on soliton of monatomic chain.

第四章，我们研究弱阻尼作用下非线性单原子链中的波动行为，首次在晶格动力学中得到了参数耗散型非线性Schrodinger方程 oDNLS方程人以及阻尼对单原子链中孤立子的影响。

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。

Secondly,under the condition of not considering the concrete values of parameters, the Gell-Mann-Okubo baryon mass relations for decuplet and octet are studied ,which are related tothe mass splittings within decuplet or octet. The higher order perturbational corrections ofSU(3) rotating excited states to GMO relations are presented up to the third order in thestandard SU(3) skyrmion quantum mechanics.

其次，在与参量具体取值无关的情况下，利用标准的SU(3)Skyrme模型，研究了孤立子转动激发态对反映重子十重态和八重态内部质量劈裂的Gell-Mann-Okubo关系式的高阶微扰修正。

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