THEORY OF NON-PROPAGATION SOLITONS INCLUDING SURFACE-TENSION EFFECTS

In this paper, the surface-tension effects to non-propagating solitons is studied. Thusthe Larraza and Putterman’s theory has (?) modified. It is found that the surface-tensionmakes the frequency range of crosswise oscillation of solitions larger, the amplitude higherand the width smaller. When the surfactension coefficient is equal to zero (a=0), theresults are consistent with those of Larraza and Putterman.     

流动对两层流体界面孤立波的影响

本文研究了两水平固壁间具有基本流动的两层不可压缩无粘无旋流体的浅水界面孤立波,利用多重尺度摄动方法求得了界面孤立波所满足的KdV方程和相应的单孤立波解,讨论了基本流动对界面孤立波的影响。     

Epidemic Dynamics with Feedback Mechanism in Exponential Networks

We introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals, Furthermore, it does not change the epidemic threshold （critical point） λc. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections.     

Evolution of Weighted Networks by Duplication-Divergence Mechanism

The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight. The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability δ, weighted, structured exponential networks are realized.     

考虑驱动及粘性时水平槽内非传播孤子

从考虑驱动和粘性条件下水平矩形槽内流体服从的非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程及其孤立子解出发，得到了驱动地孤立子所做的功及孤立子总机械能的表达式，进而证明了文献（８）中提及的λ＝＋１型孤立子是存在的，而λ＝－１型孤立子并地对应的物理实在。     

群色散光纤中高强度光脉冲传输与压缩的研究

考虑非线性四阶折射率,推导了光脉冲在群色散单模光纤中传输的非线性方程,并得到孤子型解析解.同时指出在Sech型光纤脉冲压缩实验中,光强度的阈值.     

边界条件对非传播孤子运动的影响

用延拓法处理了非线性边值问题.指出第一类和第二类边界对非传播孤子的影响分别等效于某种势垒或势阱对经典弹性粒子的作用.研究了一对反相孤子在边界作用下的运动规律并得到与实验一致的结果. 关键词：     

氢链系统中的非线性问题

考虑氢原子之间的非谐相互作用,分别用代数方法和变分法求得氢链系统中扭结与反扭结孤波解,解的特点是在非谐项的影响下,正孤波与反孤波不再对称,从而解释了实验中观察到的冰分子中L缺陷和D缺陷的对称性破缺现象,进一步的计算表明,由于非谐项的存在,正孤波与反孤波携带的能量也失去对称性,且代数方法和变分法给出一致的结果.     

光纤孤子间的相互作用

用最小作用量原理导出了非线性Schr?dinger方程两个孤子间的相互作用它作为孤子间距△与初位相差δ的函数揭示出来，当两个孤子δ<π/2时相互吸引,δ>π/2时相互排斥，δ=π/2时几乎不存在相互作用；相互作用的大小随△的增大而指数地衰减.本文的结果与实验的定量比较表明两者符合甚好