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孤立子
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  相似匹配句对
     Interaction of Solitary Waves
     孤立子的相互作用
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     Davydov Solitons
     Davydov孤立子
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  isolated subsystem
So the decentralized stabilization of such systems can be got by only appropriately designing or modifying the structure of each isolated subsystem, no matter how complicated the interconnected structure of the overall system is.
      
When a set of orbitals for the isolated subsystem have been chosen, the localized supersystem orbitals are obtained by minimizing the sum of the least-square deviations from the isolated subsystem orbitals.
      
The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions.
      
The major position in the article is that extension must be dealt with as part of a total agricultural-development process rather than an isolated subsystem for transferring technology to farmers.
      
It is clear that these connections are only one aspect of a complete system, but we believe it worthwhile to study the isolated subsystem.
      
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This review paper summarizes the international and national current status of the researches of solitons and the nonlinear evolution equations(NEEs), such as the KdV equation, MKdV equations, the self-induced-transparency-equations, the sine-Gordon equation, the nonlinear Schrodinger equation, and the Hirota equation that exhibit soliton solutions. We pay particular attention to the very important "inverse scattering transform (IST) method" whereby the initial value problem (IVP) for a nonlinear wave system...

This review paper summarizes the international and national current status of the researches of solitons and the nonlinear evolution equations(NEEs), such as the KdV equation, MKdV equations, the self-induced-transparency-equations, the sine-Gordon equation, the nonlinear Schrodinger equation, and the Hirota equation that exhibit soliton solutions. We pay particular attention to the very important "inverse scattering transform (IST) method" whereby the initial value problem (IVP) for a nonlinear wave system of partial differential equations (nonlinear evolution equations) can be solved exactly by solving a succession of linear problems.

本文综述国内外关于孤立子和显示有孤立子解的非线性进化方程(诸如KdV方程、MKdV方程、自透射方程、Gordon正弦方程、非线性Schrodinger方程和广田方程)的研究现状,特别着重介绍非常重要的“逆散射法”(IST法),借助这个方法一个非线性波动偏微分方程组(非线性进化方程)的初值问题可以通过解一系列线性问题而获得精确解。

This is a brief summary (from a theoretical view point) of the investigatomon the 'image of logical rpace'. The main content includes: (1) Mathematical analysis of the structural properties of n-dimensional logical space and that of n-element logical function. The one-to-one correspondence between this space and this function has been verified and the following principles were obtained: the set cardinal numbor of m-dimensional sub-space |α~m|=[n!/((n-m)!m!)]2~(n-m), the characteristic number of n-dimensional...

This is a brief summary (from a theoretical view point) of the investigatomon the 'image of logical rpace'. The main content includes: (1) Mathematical analysis of the structural properties of n-dimensional logical space and that of n-element logical function. The one-to-one correspondence between this space and this function has been verified and the following principles were obtained: the set cardinal numbor of m-dimensional sub-space |α~m|=[n!/((n-m)!m!)]2~(n-m), the characteristic number of n-dimensional logical space also (2) Basing on the principlc of equality and using the method of 'm-dimensional set of the α-dimensional sub-image of k order' and the method of 'm-dimensional set of k order of the α-dimensional sub-image' a simplified image of a poly- dimensional logical space was obtained. (3) Analysis of the simplification of logical function gives the following two results: thus putting forward a general program of a simplified logical function: 'the isolated and non-recurring sub-spaces are taken one after another from f.This is done from low dimension to high dimension, in other words, it is done in the order of increasing number of dimensions until all the points are taken.'

本文是关于“逻辑空间图象”理论研究的一个小结.主要内容:1.从解析角度分析了n维逻辑空间及n元逻辑函数的结构性质,论证了二者之间的一一对应关系.其中,得到了m维子空间的集合的基数|α~m|=[n!/((n-m)!m!)]2~(n-m),n维逻辑空间的示性数X(P)=sum from K=0 to n(-1)~k|α~k|=1,以及|α~0|=|γ~0|=2~n,|α~m|=|γ~m|=[n!/((n-m)!m!)]2~(n-m)|α|=sum from m=0 to n|α~m|=|γ|=sum from m=0 to n|γ~m|=3~n等定理.2.根据等价原理,采用“k阶a维子图的m维集合”及“a维子图的k阶m维集合”两种方法,得到了简明的多维逻辑空间图象。3.分析了逻辑函数的化简,得到了二个结果.从而提出了一个化简逻辑函数的普遍程序:“由低维到高维,按次序地提取f中的不重复孤立子空间,直到提完所有的点为止”。

Baoklund transformation plays an important role in the study of soliton theory. In literature, the ordinary methods to derive Backlund transformation of equation are three methods first obtained by Clairin, Chen and Hirota, respectively. In this paper, another interesting way was found for this purpose, that is converting a known Backlund transformation for some equation into a new one for another equation by using the invertible Baeklund transformation of these two equations. The Backlund transformations for...

Baoklund transformation plays an important role in the study of soliton theory. In literature, the ordinary methods to derive Backlund transformation of equation are three methods first obtained by Clairin, Chen and Hirota, respectively. In this paper, another interesting way was found for this purpose, that is converting a known Backlund transformation for some equation into a new one for another equation by using the invertible Baeklund transformation of these two equations. The Backlund transformations for the Burgers equation and for a generalized sine-Gordon equation were considered as examples. The decomposition formulae of these two Backlund transformations were obtained at the same time.

孤立子(soliton)的发现是近年来应用数学领域的一项重大进展,Backlund变换在孤立子理论研究中起着重要作用。文献中寻求方程的Baoklund变换常用的方法有Clairin法(见文[1]所用),Chen 法,Hirota 法。本文利用联系二个方程的可逆(invertible)Baoklund变换,将一个方程的自(auto-)Baoklund变换转换成另一个方程的自Baoklund变换。关于Burgers方程和广义sin-Gordon方程的两个实例表明,这显然又是一条有意义的途径。本文同时还考虑了这两个方程的Baoklund变换的分解,这对发挥Baoklund变换的功用是重要的。

 
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