色散缓变光纤对皮秒光孤子的压缩效应

本文从描述超短光脉冲在色散缓变光纤(FSDD)中传输所满足的准非线性Schrodinger(NLS)方程出发,证明该方程与常规光纤中含增益效应时的NLS方程等价,并在此基础上进行了理论分析,讨论了光弧子脉冲在不同FSDD中的传输特性;最后采用数值模拟方法研究了高阶皮秒光孤子在不同FSDD中的压缩效应,发现利用FSDD和弧子压缩效应不但可以获得更高压缩率弧子光脉冲,而且可以有效地缩短所需的光纤长度。     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Solitons for a generalized variable-coefficient nonlinear Schrdinger equation

In this paper,we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear Schrdinger equation (NLS) with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions,one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results,some previous one-and two-soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one-and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

Effect of Varying Dzyaloshinskii-Moriya Interaction on the Bistable Nano-Scale Soliton Switching

The effect of Dzyaloshinskii-Moriya (D-M) interaction on the bistable nano-scale soliton switching offers the possiblity of developing a new innovative approach for data storage technology. The dynamics of Heisenberg ferromagnetic spin system is expressed in terms of generalized inhomogeneous higher order nonlinear Schrödinger (NLS) equation. The bistable soliton switching in the ferromagnetic medium is established by solving the associated coupled evolution equations for amplitude and velocity of the soliton using the fourth order Runge-Kutta method numerically.     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e.Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.``     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e. Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N +1)-dimensional nonlinear Schro¨dinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.     

Exact chirped multi-soliton solutions of the nonlinear Schr(o)dinger equation with varying coefficients

In this letter, exact chirped multi-soliton solutions of the nonlinear Schr(o)dinger (NLS) equation with varying coefficients are found. The explicit chirped one- and two-soliton solutions are generated. As an example, an exponential distributed control system is considered, and some main features of solutions are shown. The results reveal that chirped soliton can all be nonlinearly compressed cleanly and efficiently in an optical fiber with no loss or gain, with the loss, or with the gain. Furthermore, under the same initial condition, compression of optical soliton in the optical fiber with the loss is the most dramatic. Also,under nonintegrable condition and finite initial perturbations, the evolution of chirped soliton has been demonstrated by simulating numerically.     

光孤子在色散缓变光纤中传输时的等价增益

从准非线性Ｓｃｈｒ?ｄｉｎｇｅｒ（ＮＬＳ）方程出发，导出了色散缓变光纤中光孤子脉冲传输所满足的与常规光纤中含增益效应等价的ＮＬＳ方程，给出了该方程的微扰解析解和光孤子脉冲宽度演化表达式。对于阶跃型单模光纤，得到了光纤几何参数与增益系数之间的一般函数关系。最后采用数值模拟方法模拟了不同色散缓变光纤中光孤子脉冲传输特性，指出色散缓变光纤不仅能补偿光纤损耗对孤子脉冲的展宽效应，而且能压缩光孤子脉冲，因而预计它可能有较广泛的应用前景。 关键词：     

Kinetic equation for a dense soliton gas

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg-de Vries and nonlinear Schr?dinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.     

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.     

具有二阶和三阶非线性一维光子晶体中的耦合模孤子

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学.从Maxwell方程出发,利用多重尺度法,导出了光学整流场与两个基频电场包络的非线性耦合模方程组,给出了耦合模方程组的孤子解.结果表明,由于二阶非线性导致的光学整流场对基频电场有调制作用,使得两个基频电场分量可以呈现为亮孤子亮孤子、暗孤子暗孤子及亮孤子-暗孤子对 当两个基频电场的振动频率趋于光子晶体频带的带边频率时,光学整流场消失     

强非局域空间光孤子大相移的理论研究以及应用方案设计

本文发展了郭旗等人的唯像理论,发现在铅玻璃中,孤子随着本身功率或者抽运光孤子功率几十个毫瓦的变化,就会出现π的附加相移.基于抽运光孤子功率对弱信号光孤子相位有着高调制灵敏度的结论,提出了一种较可行的光开关实现方案. 关键词： 强非局域 空间光孤子 大相移     

Matter-Wave Solitons in Two-Dimensional Bose-Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.     

Solitary waves in the resonant nonlinear Schrödinger equation: Stability and dynamical properties

The stability and dynamical properties of the so-called resonant nonlinear Schrödinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrödinger (NLS) equation with the addition of a perturbation used to describe wave propagation in cold collisionless plasmas. We first examine the modulational stability of plane waves in the RNLS model, identifying the modifications of the associated conditions from the NLS case. We then move to the study of solitary waves with vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright soliton solutions depending on the relative signs of dispersion and nonlinearity. The corresponding existence, stability and dynamics of these solutions are studied systematically in this work.     

基于耗散孤子种子的啁啾脉冲光纤放大系统输出特性

以不同滤波器带宽下获得的全正色散光纤激光器耗散孤子作为啁啾脉冲放大(CPA)系统的种子脉冲, 研究了光栅对和光纤展宽器CPA系统输出脉冲的可压缩性. 结果表明, 对于大能量耗散孤子种子脉冲, 当CPA系统采用正色散光纤展宽器时, 光纤群速色散与自相位调制之间的相互作用不仅可抑制耗散孤子脉冲光谱调制的影响, 还可使脉冲在光纤展宽器中自相似演化, 从而可提高CPA输出脉冲的可压缩性. 通过优化光纤展宽器长度, 对于耗散孤子种子源, 采用光纤展宽器的CPA系统输出脉冲可压缩性与主脉冲所占脉冲总能量之比均优于采用光栅对展宽器时的情况.     

Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities

In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions.     

用行波解法研究非线性偏振旋转控制光孤子系统

采用行波解法求解了将非线性偏振旋转控制机构作为强度滤波元件接入滤波控制光纤孤子系统的非线性薛定谔(NLS)方程,得到了近似形式的解析解,并得到了孤子振幅、中心位置、相位的演化方程,在此基础上研究了孤子系统的稳定性问题和孤子系统中由于滤波器带来的非孤子成份等问题.