五阶克尔非线性光纤放大器中光脉冲的传输特性

以变系数高阶非线性薛定谔方程为理论模型,对光脉冲在具有五阶非线性克尔效应光纤放大器中的传输特性进行了研究.在加入振幅微扰、相位扰动、噪声微扰的情况下,数值模拟了亮孤波、灰孤波和黑孤波在光纤系统中的传输稳定性,并且讨论了孤子间的相互作用.数值模拟结果表明:在有限的微扰下,三种光脉冲具有良好的传输稳定性.     

微扰法求解铅玻璃中的涡旋空间光孤子

在量子力学的微扰理论框架下,利用微扰法求解得到了1+2维强非局域非线性介质——铅玻璃中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的近似解析解。从非局域非线性薛定谔方程(NNLSE)出发,以铅玻璃中的真实折射率与Snyder-Mitchell(SM)模型中描述的抛物线型折射率的差值为微扰,以SM模型中的拉盖尔高斯孤子解为基态解,求得了铅玻璃材料中二阶微扰修正的"类拉盖尔高斯型"涡旋孤子的解析解。拓扑荷值分别为1、2、3、4的微扰修正的"类拉盖尔高斯型"光孤子比未加微扰的拉盖尔高斯型光孤子更稳定,非常接近孤子真解的传输行为。     

正弦周期信号微扰实现的混沌控制

研究了用正弦周期信号对非线性系统变量进行微扰，从而实现混沌控制的方法。研究结果表明，当外加周期信号的频率落入混沌系统的频带内，且微扰强度足够大时，可使混沌系统出现稳定的周期解。     

稳态光折变空间孤子传输的量子理论

稳态光折变空间孤子系统可用奇异Lagrange量描述，系统含Dirac约束.通常按对应原理写 出孤子系统的量子对易关系和量子运动方程时，未计及约束.对稳态光折变空间光孤子约束 系统进行Dirac括号量子化，给出了系统的对易关系和量子场方程.在线性近似下给出量子 非线性薛定谔方程的微扰解，并讨论了孤子的压缩性质. 关键词： 量子场论 量子光学 光折变空间孤子 压缩效应     

水槽中孤波相互作用的微扰变分分析

对Wu等人所观察到的水槽孤波相互作用的现象,给出了微扰变分解析分析,所得结果初步解释了水槽中孤波相互吸引和相互排斥现象,同时给出了同相双孤波的合并周期和第一次合并时间,孤子间的相互作用力及相互作用势,为孤波相互作用提供了粒子描述。 关键词：     

矢量孤波在综合管理的双折射光纤系统中的传输

以变系数的耦合非线性薛定谔方程作为光脉冲传输的理论模型,考虑了三阶色散、自频移效应、自陡峭效应和五阶非线性效应,采用对称分步傅里叶方法,数值模拟了矢量组合孤波在综合管理的双折射光纤中的传输,研究了矢量组合孤波中相邻孤子间的相互作用,并且讨论了在加入噪声干扰、功率微扰和相位微扰情况下矢量组合孤波的传输稳定性。模拟结果显示:在一定条件下,矢量组合孤波中相邻两孤子几乎不发生相互作用,能够无畸变传输;并且在有限干扰情况下,矢量组合孤波具有良好的传输稳定性和抗干扰性。     

槽中双孤子互作用的微扰求解

孤子运动的Miles方程是一个具特征的非线性Schrdinger型方程.借求孤子解的微扰法,导出所遵循的矩阵方程,和孤子解的修正量δu(x,λ).并据双孤子解,计算了它的周期互作用状态 关键词： Miles方程 微扰双孤子解     

复色光伏孤子的稳定性

给出求解复色孤子半高宽的近似方法，该方法对分析复色光束的演化提供一个定性的基础 .进一步的数值模拟结果表明，当入射双曲正割光束满足复色光伏孤子半高宽与中心光强的 关系时，双曲正割光束在晶体中的传播就非常接近孤子，表明复色光伏孤子对于小的微扰是 稳定的.此外，复色光伏孤子对于小的轴偏离具有较好的稳定性；复色光伏孤子对因温度微 扰引起折射率变化的情况也具有较好的稳定性.一般情况下，初始光强分布接近复色光伏孤 子光强分布的两束光的光强在传播过程中不断地起伏，形成呼吸状结构，但如果入射面处的 光强明显偏离孤子的光 关键词： 复色光伏空间孤子 稳定性     

耦合复变系数Ginzburg-Landau方程的啁啾类孤波对传输特性研究

通过对耦合复变系数Ginzburg-Landau方程所描述的非线性光纤系统的研究,分别数值分析了啁啾类亮-暗和啁啾类暗-暗两组孤波对在这种非线性光纤中传输的稳定性.在加入非线性增益(损耗),和增益带宽限制放大(滤波的谱限制)效应后,耦合啁啾孤子对的特点是暗孤波在反常群速度色散区,亮孤子在正常群速度色散区时可以稳定传输.并进一步讨论了加入振幅微扰和白噪声微扰对孤子传输稳定性的影响.     

用自适应脉冲微扰引导混沌系统到周期解

用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词： 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.     

Soliton and chaotic structures of dust ion-acoustic waves in quantum dusty plasmas

The quantum hydrodynamic model is employed to study the soliton and chaotic structures of dust ion-acoustic waves in quantum dusty plasmas consisting of electrons, ions, and negatively/positively charged dust particles. By means of the reductive perturbation technique, two-dimensional Davey-Stewartson (DS) system is derived. By improving the extended projective method and the extended tanh-function method, a separation of variables solution with arbitrary functions for the Davey-Stewartson system is obtained. Many soliton and chaotic structures such as localized nonlinear coherent structure, line-soliton structure, periodic wave pattern structure, Rössler and Lorenz chaotic structures are given. It is found that these structures are effected by the quantum effects.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Controlling chaos in a high dimensional system with periodic parametric perturbations

The effect of applying a periodic perturbation to an accessible parameter of a high-dimensional (coupled-Lorenz) chaotic system is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic system can result in limit cycles or significantly reduced dimension for relatively small perturbations.     

Nonlinear Schrödinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrödinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport.     

Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

周期参数扰动的T混沌系统同宿轨道分析

针对一类周期参数扰动的T混沌系统, 通过变换将系统转化为具有广义Hamilton结构的周期参数扰动的慢变系统, 运用Melnikov方法对系统的同宿轨道进行了分析计算, 并给出了系统的同宿轨道参数分支条件. 同时, 通过数值实验, 对周期参数扰动控制策略及同宿轨道进行了仿真, 验证了文中理论分析的正确性. 关键词： Hamilton系统 Melnikov方法 同宿轨道 周期参数扰动     

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.