KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Soliton Dynamics of NLS Equation at the Presence of Perturbations

A new direct approach based on the separation of variables for soliton perturbations is developed. With the aid of this approach, the effects of perturbation on a soliton of nonlinear Schrödinger (NLS) equation is obtained. In comparison with other direct methods,our approach is very concise and easy to be understood. Besides, no more approximation is employed except for the linearization of the perturbed NLS equation.     

TDGL方程的微扰理论

在一阶近似下,获得了微扰对TDGL(TimeDependentGinzburgLandau)方程的静态孤子解的影响,即求得了孤子参数随时间慢变量的变化情况和一阶修正的一般表达式,以及一个特例的具体表式 关键词： 静态孤子 孤子微扰论     

Approximation of the soliton solution for the generalized Vakhnenko equation

A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.     

An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Holm equation is obtained. One-loop soliton solution of the Degasperis-Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.     

Phase Transition in the Chiral Quark Soliton

Chiral symmetry phase transition is studied by making use of the finite temperature Green's function and the path integral approach in the chiral soliton model. The temperature-dependent effective potential is obtained in the one-loop approximation, including quark and σ-, π-meson loop. The critical temperature-versus the nuclear density is calculated. At zero baryop density the critical temperature is 172 MeV. In nuclear medium it is found that the critical temperature decreases fast when the nuclear density is increasing.     

双曲正割光束在弱非局域非线性体材料中的传输特性研究

利用变分法研究了(2+1)维圆对称双曲正割光束在弱非局域非线性介质中的传输,得到了描述光束束宽、相位、波前曲率、振幅演化的一组微分方程,并得到了光束做孤子传输的临界功率;通过稳定性分析给出了弱非局域情形非局域效应对光束传输的稳定作用的定量描述,从而自洽地阐述了由不稳定的(2+1)维克尔孤子到稳定的(2+1)维弱非局域孤子的过渡情形. 数值模拟的结果验证了变分计算结果的正确性,并说明圆对称的双曲正割函数是(2+1)维弱非局域空间孤子的很好的近似. 关键词： 双曲正割光束 弱非局域非线性介质 空间光孤子     

Motion of Solitons in Deoxyribonucleic Acid (DNA) Double Helices with Dissipation

Under the first-order approximation, the general soliton solution of the plane base rotator model is obtained using the direct perturbation method, when taking the dissipation interaction in the DNA double helices dynamics into consideration. The stability condition of system leads to a relation among the soliton velocity, the coupling constants and the damping factor. It imposes limits to the maximum value of the soliton velocity and energy. An estimation of the value of the dissipation factor is given using recently published experimental data. Some practical problems such as the energy transmission and the semiconservative replication of B-DNA are discussed in detail.     

受扰动的光纤孤子间的相互作用

基于含扰动的非线性薛定谔方程，发展了高登的光孤子相互作用理论，直接从近似的二孤子解昨到描述实际光纤通讯中孤子间的相互作用的解析公式，公式表明在实际的通讯系统中光纤孤子间的相互作用不令依赖于它们之间相对相差，而且依赖于它们的相对能量，速度差随传输距离的变化。     

Optical soliton with group delay in microring coupled-resonator optical waveguides

This paper derives the dispersion relation of microring coupled-resonator optical waveguides (CROWs) without any approximation by using the transfer matrix method. Based on the established dispersion relation of CROWs it obtains the slow group velocity and dispersion coefficient. It finds that the effect of dispersion on optical pulses can be adjusted to balance the effect of nonlinearity by changing coupling coefficient or loss, so optical soliton with group delay can be obtained in microring CROWs. The optical soliton with group delay is of great significance for applications of microring CROWs in delay lines and optical buffers of future all-optical communication systems.     

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrdinger equation analytically by performing the Hirota's bilinearization method. The precise expression of a parameter , which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton (∈2≠1) while it has no effects on the wave central position.Moreover, the precise expressions of a nonautonomous black soliton's (∈2≠1) width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton's evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.     

Interaction of in-band and in-gap lattice soliton trains in optically induced two-dimensional photonic lattices

We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons (IBSs) and gap soliton trains (GSTs), in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the $\pi$-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The `negative refraction' effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.     

Influence of Randomly Varying Birefringence on Soliton Switching

In this paper, the effects of the randomly varying birefringence on soliton switching in the twin-core fiber are discussed through a nonlinear coupling equation , some novel and useful results on soliton switching are obtained.     

强色散补偿有耗光纤链中孤子的稳定传输

用平均近似的方法,得到了孤子在强色散有耗光纤链中演化的相图.在分析相图的基础上,提出了一个可使孤子保持稳定传输的新相图.按照这个新相图,给出了孤子稳定传输的参量.这些参量,通过数值运算,在我们感兴趣的区域里得到了验证.     

α-螺旋蛋白质分子链上的孤立子寿命

以连续近似条件下的孤立子为初始条件,对α-螺旋蛋白质分子链上动力学方程的数值解进行了讨论,发现在不考虑热振动影响的情况下,α-螺旋蛋白质分子链上孤立子的寿命仍是有限的.     

初始啁啾对光孤子压缩态的影响

在线性近似条件下，量子化了非线性薛定谔方程，用后向传播数值求解了初始啁啾对光孤子压缩比的影响，数值结果表明，初始正啁啾在初始一定距离范围内能减小压缩比，理想光孤子的压缩效果最好。     

Spatial Dark Solitons in an Atom Laser Beam

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｔｅｒｆｅｒｅｎｃｅｂｅｔｗｅｅｎｔｗｏＢｏｓｅＥｉｎｓｔｅｉｎｃｏｎｄｅｎｓａｔｅｓ［１］ｈａｖｅｇｒｅａｔｌｙｓｔｉｍｕｌａｔｅｄａｉｎｔｅｒｅｓｔｉｎｔｈｅｒｅａｌｉｚａｔｉｏｎｏｆａｎａｔｏｍｌａｓｅｒ［...     

双折射光纤中色散管理孤子研究

研究色散管理孤子在双折射光纤中的传输特性.应用变分法分析并给出了双折射光纤中色散管理孤子参量演化的常微分方程.数值分析双折射对孤子参量的影响,分析发现在双折射光纤中色散管理孤子的宽度和啁啾不再是严格周期性变化.在色散管理的同时进行周期性偏振补偿可以消除走离效应,可以产生管理孤子.     

The Strong Interaction in Chromodynamics Ⅱ

A static soliton solution is obtained from the field equations of chromodynamics. The relativistic wave equation for meson states in which the quark and antiquark interact through the intermediary of this gluon field gives rise. to the same wavefunction and mass spectra obtained before under the independent particle approximation. The calculated values of mass difference of η_c and Ψ/J particles and mass difference of Ψ(3685) and Ψ(3770) due to spin-dependent part of the interaction are in good agreement with the experiment.     

脉冲内拉曼散射影响下的孤子之间的相互作用及其控制

研究了脉冲内拉曼散射效应影响下的同相和反相相邻孤子脉冲之间的相互作用,分析了孤子之间的相互作用对定时抖动的影响和脉冲内拉曼散射效应对孤子频移的影响。研究结果表明:在脉冲内,在拉曼散射效应的影响下,同相基态孤子脉冲的周期性离合被破坏了,两孤子脉冲一次碰撞后一直处于排斥状态,并且在碰撞后自频移现象十分明显;反相孤子脉冲的影响则较弱,两孤子脉冲都向下降沿发生偏移。引入非线性增益可以有效地控制孤子之间的相互作用,抑制自频移效应和稳定孤子传输。