周期背景下怪波的激发和调制

为了研究怪波在周期背景中的激发和演化情况,以含有周期外势的自聚焦非线性薛定谔方程为模型,采用快速分步傅里叶算法,讨论了在两种周期势(实势和复势)的情况下,怪波的激发和演化情况.研究表明:在两种周期势背景下都能通过平面波加微扰来激发怪波;在实周期背景下,通过改变周期势的振幅和周期能够产生不同的光学现象;在复周期背景下,通过同样的初始波能够激发一种超大怪波,而且实部振幅对怪波具有能量耗散和减速作用,虚部振幅对怪波具有能量增益和加速作用,选择合适的实部振幅与虚部振幅可以产生强度不同的大怪波.研究结果有助于在光晶格中捕获和调节怪波,以及获得高功率波.     

有限宽度背景中的啁啾灰孤子

基于在正常色散区的变系数非线性薛定谔方程,考虑一个带有微扰的参数渐减光纤系统,并利用数值模拟方法,对超高斯型有限宽度背景波和有限宽度背景中啁啾灰孤子的传输进行详细地研究.结果表明,超高斯背景波可以在带有微扰的参数渐减光纤系统中不受负载啁啾灰孤子的影响而稳定传输.当取背景波脉宽与啁啾孤子的初始脉宽比例大于或等于50时,有限宽度背景中啁啾灰孤子的数值结果基本与精确解相吻合.即使选取的背景波脉宽不宽,有限宽度背景中的啁啾灰脉冲仍可以很好的保持其孤子性质.     

Characteristics of Rogue Waves on a Soliton Background in the General Coupled Nonlinear Schrödinger Equation

Under investigation in this work is the general coupled nonlinear Schrödinger (gCNLS) equation, which can be used to describe a wide variety of physical processes. By using Darboux transformation, the new higher-order rogue wave solutions of the equation are well constructed. These solutions exhibit rogue waves on a multi-soliton background. Moreover, the dynamics of these solutions is graphically discussed. Our results would be of much importance in enriching and predicting rogue wave phenomena arising in nonlinear and complex systems.     

Soliton and Rogue Wave Solution of the New Nonautonomous Nonlinear Schrödinger Equation

In this paper, a new type (or the second type) of transformation which is used to map the variable coefficient nonlinear Schrödinger (VCNLS) equation to the usual nonlinear Schrödinger (NLS) equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is
introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically.
The main differences between the two types of transformation mentioned above are listed by three items.     

Bright Solitons on Continuous Wave Background in Blood Vessels

The nonlinear Schr6dinger equation （NLSE） with variable coefficients in blood vessels is discussed via an NLSE-based constructive method, and exact solutions are obtained including multi-soliton solutions with and without continuous wave backgrounds. The dynamical behaviors of these soliton solutions are studied. The solitonic propagation behaviors such as restraint and sustainment on continuous wave background are discussed by altering the value of dispersion parameter δ. Moreover, the longitude controllable behaviors are also reported by modulating the dispersion parameter ＆ These results are potential1y useful for future experiments in various blood vessels.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking(OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity(QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Motion of a Bose-Einstein Condensate Bright Soliton Incident on a Step-Like Potential

The motion characteristics of a Bose-Einstein condensate bright soliton incident on a local step-like potential barrier are investigated analytically by means of the variational approach. The dynamics of the soliton-potential interaction is studied as well. Then the results are verified by direct numerical simulations of the Gross-Pitaevskii equation. It is found that a moving bright soliton can be reflected from or pass over a step-like potentiaI in a controllable fashion, the critical velocity depends on the width of the soliton and the parameters of the step, and the motion trajectory of the soliton does not depend on its phase. The atom density envelope of the soliton is changed as the result of the interaction between the soliton and the step-like potential.     

光纤中双孤子相互作用的等价粒子理论

本文给出了含有一般扰动的非线性薛定锷（Ｓｃｈｒｏｄｉｎｇｅｒ）方程的孤子等价粒子理论，它使人们对孤子的粒子性质有了更深的了解，同时给出了光纤中双孤子相互作用的等价粒子分析，得到了与基于逆散射及微扰变分法完全一致的结果，这一方法可用于多孤子相互作用的解析分析，并能给出这一过程的直观物理图象．     

Properties of Controllable Soliton Switching in Optical Lattices with Longitudinal Exponential-Asymptotic Modulation

The properties of controllable soliton switching in Kerr-type optical lattices with different modulation are investigated theoretically and simulated numerically. The results show that the optical lattices can be available for all-optical soliton switching through utilization for length-scale competition effects. And through longitudinal exponential-asymptotic modulation for the linear refractive index, the properties of soliton switching in the optical lattices can be improved. The number of output channels of soliton switching can be controlled by the parameters such as incident angle, asymptotic rate of longitudinal modulation, guiding parameter and form factor.     

基于脉冲对交叉相位调制的亮脉冲的压缩

提出了一种利用色散位移光纤(DSF)压缩波长位于光纤正常色散区的亮脉冲的方法.即让亮脉冲与一个中心波长位于光纤反常色散区的强脉冲对在光纤中共同传输,在适当条件下,交叉相位调制(XPM)效应会导致亮脉冲的压缩.通过分步傅里叶方法(SSFM)对这一压缩过程进行数值模拟和分析,结果表明高斯脉冲的脉宽被压缩了9.8倍,峰值功率增加了6.5倍,且该方法可以有效地避免脉冲走离效应,使脉冲获得更好的压缩效果.     

Higher-Order Rogue Wave Solutions to a Spatial Discrete Hirota Equation

The higher-order rogue wave(RW) for a spatial discrete Hirota equation is investigated by the generalized(1,N-1)-fold Darboux transformation. We obtain the higher-order discrete RW solution to the spatial discrete Hirota equation. The fundamental RWs exhibit different amplitudes and shapes associated with the spectral parameters. The higher-order RWs display triangular patterns and pentagons with different peaks. We show the differences between the RW of the spatially discrete Hirota equation and the discrete nonlinear Schr?dinger equation. Using the contour line method, we study the localization characters including the length, width, and area of the first-order RWs of the spatially discrete Hirota equation.     

一种新型光格子中孤子的控制(英文)

本文数值研究了一种纵向呈周期性指数调制的克尔非线性光格子中空间孤子的控制和导向.结果表明,这种光格子能提供更大范围的孤子控制,通过合理设计光格子的参数如光格子的深度、横向调制频率、纵向调制周期以及输入波束的参数可以实现孤子的控制.     

Interaction between Breathers and Rogue Waves in a Nonlinear Optical Fiber

We study the interaction between breather and N-order rogue waves in a nonlinear optical fiber.The impacts of the relative phase and the interaction distance between breathers and rogue waves are discussed in detail.Specifically,the breather can reduce the maximum hump value of high-order rogue waves greatly in the cases of nonzero relative phase or nonzero interaction distance.The characteristic of exclusion between breathers and rogue waves is described qualitatively in the situation of different interaction distances,which can be used to change the temporal-spatial distribution of rogue waves.Their interaction properties are characterized by the trajectory of localized waves' valleys and humps.It is shown that the interaction changes the dynamical evolution trajectory of rogue waves and breathers.These results provide some possible ways to control high-order rogue waves.     

Rogue Wave Solutions for Nonlinear Schrödinger Equation with Variable Coefficients in Nonlinear Optical Systems

In this paper, the generalized Darboux transformation is constructed to variable coefficient nonlinear Schrödinger (NLS) equation. The N-th order rogue wave solution of this variable coefficient NLS equation is obtained by determinant expression form. In particular, we present rogue waves from first to third-order through some figures and analyze their dynamics.     

光温双控太赫兹波调制特性研究

基于多频带金属开口谐振环结构,利用GaAs材料的光敏特性和VO₂薄膜的热致相变特性,设计了一种既能实现光控又能实现温控的太赫兹(Terahertz, THz)波调制器,研究了光强和薄膜温度对 THz波调制特性的影响。结果表明,随着光强的增加,谐振频率均出现蓝移且谐振强度减小,当光强达到0.2 μJ·cm-2时,第二个谐振点(0.52 THz)蓝移了0.14 THz,透射幅度增加达50%;随着VO₂温度增加至相变温度以上,THz波透射幅度急剧减小,在0.63 THz处透射幅度减小达45.5%;当光强和温度同时控制时,随着光强和温度的增加,谐振点频率蓝移且谐振点处的THz波透射幅度增加,但在温度超过相变温度后,则温度控制起主导作用。设计的THz波调制器能通过光控和温控实现对THz波的明显调制效果,可为实现多功能的THz波功能器件的设计及应用提供参考。     

Interaction between Soliton and Periodic Wave

A truncation for the Laurent series in the Padnleve analysis of the KdV equation is restudied. When the truncation occurs the singular manifold satisfies two compatible fourth-order PDEs, which are homogeneous of degree 3. Both of the PDEs can be factored in the operator sense. The common factor is a third-order PDE, which is homogeneous of degree 2. The first few Invariant manifolds of the third-order PDE are studied. We find that the invariant manifolds of the third-order PDE can be obtained by factoring the invariant manifolds of the KdV equation. A numerical solution of the third-order PDE facts about the third-order PDE. is also presented. The solution reveals some interesting