从稳定孤子到混沌型格点孤子的宏观实验研究

近30年来,由于孤立子现象在物理学的几乎所有领域得到了广泛应用,孤立子的理论、实验和应用研究成为一个重要的热门研究课题.孤立子的直接宏观观察是人们一直感兴趣的重要问题.自从1984年吴君汝等在振动台上观察到了狭长槽内非传播流体孤子以来,振动台上的非线性体系的宏观实验给我们提供了一个很好的实验场所.宏观“单原子”格点体系的各种激发为Denardo等所观察到.文献[5]给出了受参数激励的颗粒体系中的局域结构.在微观系统,对双原子非线性格点系的研究揭示了更丰富的孤子结构.相应的参数激励下宏观双原子格点体系的各种模式也被观察到.

双折射光纤中三阶色散对孤子稳定性的影响

:本文研究了单模光纤中双折射效应和高阶色散效应对孤子传输稳定性的影响。研究结果表明 :线性双折射所导致的两偏振孤子分离的振幅阈值受三阶色散的影响而增大 ,如果输入脉冲振幅在阈值以上 。

双曲Yamabe流的精确解

得到了双曲Yamabe流的一些精确解.第一类解是具有初始度量为Einstein的解,第二类解是具有轴对称的解.最后,作为这种流的特殊解,定义了稳定双曲Yamabe孤子,而且得到了这种孤子解所满足的方程.

耗散双曲Yamabe流的精确解

本文介绍了一种新的几何流,得到了这种流的一些精确解.首先得到了初始度量为Einstein的解.其次得到了具有轴对称的解.最后,作为这种流的特殊解,定义了稳定耗散双曲Yamabe孤子,而且给出了这种孤子解所满足的方程.

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge–Kutta method and physical parameter values appropriate to the α-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.

Two-Dimensional Soliton Interaction for Multi-component Bose-Einstein Condensates

For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev-Petviashvili-Ⅰ equation at the lowest order from the originai coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev- Petviashvili-1 equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.

Bio-energy in s-Helix Protein Molecules with Three Properties of Soliton-Transported Channels

We study numerically the propagating properties of soliton-transported bio-energy excited in the a-helix protein molecules with three channels in the cases of the short-time and long-time motions and its features of collision at temperature T = 0 and biological temperature T = 300 K by the dynamic equations in the improved Davydov theory and fourth-order Runge-Kutta method, respectively. From these simulation experiments we see that the new solitons in the improved model can move without dispersion at a constant speed retaining its shape and energy in the cases of motion of both short-time or T = 0 and long time or T = 300 K and can go through each other without scattering in their collisions. In these cases its lifetime is, at least, 120 ps at 300 K, in which the soliton can travel over about 700 amino acid residues. This result is consistent with analytic result obtained by quantum perturbed theory in this model. In the meanwhile, the influences of structure disorder of a-helix protein molecules, including the inhomogeneous distribution of amino acids with different masses and fluctuations of spring constant, dipole-dipole interaction, exciton-phonon coupling constant and diagonal disorder, on the solitons are also studied by the fourth-order Runge-Kutta method. The results show that the soliton still is very robust against the structure disorders and thermal perturbation of proteins at biological temperature 300 K. Therefore we can conclude that the new soliton in the a-helix protein molecules with three channels is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.

热非局域非线性高阶界面孤子的多种孤子解

讨论了是光束在(1+1)维的热致非局域介质中的传输,此介质在中心处被分为两部分,两部分的线性折射率是不同的.发现在中心处的界面附近存在多阶稳定的界面孤子.本文研究的是五阶和六阶界面孤子,它们都存在三种不同的孤子解.三种孤子解的波形、束宽、光束重心、存在和稳定区间都是不相同的.五阶孤子的三种解都存在稳定区间,并且其中两个解存在共同稳定区域.然而六阶孤子只有其中一种解存在稳定区间.

Geometry of Ricci Solitons

Ricci solitons are natural generalizations of Einstein metrics on one hand, and are special solutions of the Ricci flow of Hamilton on the other hand. In this paper we survey some of the recent developments on Ricci solitons and the role they play in the singularity study of the Ricci flow.