单摆链上的孤子波演示

从扭转弹性棒上的单摆链导出了SineGordon方程,该方程有孤子解.用橡皮筋和大头针制成的简单单摆链机械系统,可演示SineGordon方程的孤子波.     

奇异物质与暗能量作用的sine-Gordon孤子星模型

研究了具有奇异物质和暗能量作用的sine-Gordon孤子星模型,根据场方程计算了物态方程的解和星体质量,发现物质密度和压强与孤子态和星体质量有关.另外,还对星体平衡和暗能量的稳定性质进行了分析和讨论,结果表明孤子星内部以奇异物质与暗能量的混合态形式存在. 关键词： 奇异物质 暗能量 sine-Gordon孤子星     

(2+1)维破裂孤子方程的多方孤子解及其混沌行为

利用投射方程法和变量分离法,得到(2+1)维破裂孤子方程的新显式精确解. 根据得到的孤立波解,利用 Weierstrassp 函数,构造出多方孤子局域结构. 利用两个混沌系统研究了破裂孤子方程的混沌行为. 关键词： 投射方程法 破裂孤子方程 多方孤子 混沌行为     

Stochastic analysis of a Hopf bifurcation: Master equation approach

The effect of inhomogeneous fluctuations in a reaction-diffusion system exhibiting a Hopf bifurcation is analyzed using the master equation approach. A Taylor expansion of the logarithm of the stationary probability, known as the stochastic potential, is calculated. This procedure displays marked analogies with the theory of normal forms. The critical potential, reduced to its local expansion around an arbitrary point of the limit cycle, brings out the essential role played by the phase of the oscillating variables. A comparison with the Langevin analysis of Walgraefet al. [J. Chem. Phys. 78(6):3043 (1983)] is performed.     

Chaotic Behavior and Instability of Perturbed sine-Gordon Solitons

Solitons of the sine-Gordon system interacting with a disturbed external field are handled by using a direct method. Theoretical analysis reveals that the single soliton perturbed by a periodic field leads to chaotic behavior of the system, and the perturbed double soliton is unstable for most of physically interesting spacetime disturbances.     

二维非定常Sine-Gordon方程辛算法及其孤子数值模拟

在矩形域[-a,a]×[-a,a]内对微分算子L=(ə²)/(əx²)+(ə²)/(əy²)用5点差分格式将二维非定常Sine Gordon方程离散化为一个2×799²阶非线性Hamilton系统.对该系统使用Euler中心格式,得到一个非线性方程组.对此方程组建立迭代解法并给出了这个迭代方法的收敛条件和收敛速度.Sine Gordon方程单孤子和双孤子的数值模拟试验显示该辛算法是有效的.     

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.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

Order and fluctuations in nonequilibrium molecular dynamics simulations of two-dimensional fluids

Finite systems of hard disks placed in a temperature gradient and in an external constant field have been studied, simulating a fluid heated from below. We used the methods of nonequilibrium molecular dynamics. The goal was to observe the onset of convection in the fluid. Systems of more than 5000 particles have been considered and the choice of parameters has been made in order to have a Rayleigh number larger than the critical one calculated from the hydrodynamic equations. The appearance of rolls and the large fluctuations in the velocity field are the main features of these simulations.     

完全可积的非线性方程建立哈密顿理论的一般方法和对SG方程应用

完全可积的非线性方程的单式矩阵的泊松括号已知可以表为对x的积分，指出被积函数一定 可以表为约斯特解对的直积的线性组合的微分，并可由直积矩阵相应元的对比确定组合系数 .从而解决了建立非线性方程哈密顿理论的一般方法.由于实验室系中的SG方程，相应的表述 异常复杂，所以以它为例来说明方法的实质.同时由于现有的相关工作违反了泊松括号同时 性的要求，给出了必要的改正. 关键词： 非线性方程 哈密顿理论 孤子     

(3+1)维Burgers系统的瞬内嵌孤子和瞬锥形孤子

利用投射方程法和变量分离法,得到了(3+1)维Burgers系统的变量分离解(包括孤波解、周期波解和有理函数解).根据孤波解和有理函数解,构造出Burgers系统新颖的局域结构,例如瞬内嵌孤子和瞬锥形孤子.     

光纤孤子包络方程及相关分析

从经典唯象观点出发,提出了相位移动的精确公式,严格推导出光纤孤子包络方程,揭示了原包络函数的唯一性,并合理分析了光纤孤子的形成机制.     

Quantization of sine-Gordon solitons on the circle: Semiclassical vs. exact results

We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function regularization in the integral representation. We compare the semiclassical results with exact numerical calculations in the literature and find excellent agreement even outside the plain semiclassical regime.     

mKdV方程的双扭结单孤子及其稳定性研究

基于双曲函数法的思想,通过选择新的展开函数,得到了modified Korteweg-de Vries(mKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为mKdV方程的扭结状或钟状孤波解.文中对双扭结型孤子解的稳定性进行了数值研究,结果表明:在长波和短波简谐波扰动、钟型孤立波扰动与随机扰动下,该孤子均稳定.     

Interaction of a Hopf bifurcation and a symmetry-breaking bifurcation: Stochastic potential and spatial correlations

The multivariate master equation for a general reaction-diffusion system is solved perturbatively in the stationary state, in a range of parameters in which a symmetry-breaking bifurcation and a Hopf bifurcation occur simultaneously. Thestochastic potential U is, in general, not analytic. However, in the vicinity of the bifurcation point and under precise conditions on the kinetic constants, it is possible to define a fourth-order expansion ofU around the bifurcating fixed point. Under these conditions, the domains of existence of different attractors, including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors, are determined analytically. The role of fluctuations in the existence and stability of the various patterns is pointed out.     

Stochastic analysis of a chemical reaction with spatial and temporal structures

A stochastic analysis of the spatial and temporal structures in the Prigogine-Lefever-Nicolis model (the Brusselator) is presented. The analysis is carried out through a Langevin equation derived from a multivariate master equation using the Poisson representation method, which is used to calculate the spatial correlation functions and the fluctuation spectra in the Gaussian approximation. The case of an infinite three-dimensional system is considered in detail. The calculations for the spatial correlation functions and the fluctuation spectra for a finite system subject to different kinds of boundary conditions are also given.     

扩展的形变映射方法和(2+1)维破裂孤子方程的新解

扩展的形变映射方法应用于非线性物理模型的研究， 获得了(2+1)维破裂孤子方程的新解, 合适地选择任意函数，可以获得该模型的丰富的局域和非局域的相干结构，这里仅揭示(2+1)维破裂孤子方程(1)和(2)的周期型新孤波结构. 关键词： 形变映射方法 (2+1)维破裂孤子方程 孤波结构     

Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation

We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.     

(2+1)维 Zakharov-Kuznetsov 方程的精确解和孤子结构

在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词： 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构