扰动对一维局域模的影响

在紧束缚模型基础上，考虑到缺陷、温度、掺杂等外界因素的影响，用方形随机分布模拟了格点原子扰动对一维局域模的影响.给出了不同扰动参数σ下，孤子和极化子中各个局域模的变化情况.计算发现，由于孤子g₁模的钉扎效应，扰动后，弱模g₄定域性会得到加强，还会产生两个新定域模g′₁和g′₂，它们与相应的g₁和g₂模有相同的节点和宇称 ；极化子的g₇模在畸变较大时将 关键词： 扰动 局域模 聚合物     

Demonstration of surface soliton arrays at the edge of a two-dimensional photonic lattice

We demonstrate surface soliton arrays at the interface between a homogeneous medium and an optically induced two-dimensional semi-infinite photonic lattice. These are nonlinear Tamm-like surface states localized in one but extended periodically in the other transverse dimension. Both in-phase and staggered out-of-phase soliton arrays are observed, and the experimental results are corroborated by numerical simulations.     

Solitons in a linear lattice with defects

Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied.     

Internal vibrations of nonlocal nonlinear Schrödinger soliton

We prove that the nonlocality is a source of the internal mode generation in a bright soliton of the nonlocal nonlinear Schrödinger equation, at least in the weak nonlocality limit. The internal mode bifurcates from the edge of the continuous spectrum of the linearized eigenvalue problem into the gap of this spectrum. A dependence of the internal mode propagation constant position in the gap on the nonlocality rate is established. It is shown that the vibration amplitude of the soliton decays inversely proportional to the propagation distance, as in the local models.     

Stability bands for moving solitons in uniform and inhomogeneous damped ac-driven circular Toda lattices

By means of systematic simulations, we study the motion of discrete solitons in weakly dissipative Toda lattices (TLs) with periodic boundary conditions, resonantly driven by a spatially staggered time-periodic (ac) force. A complex set of alternating stability bands and instability gaps, including scattered isolated stability points, is revealed in the parametric plane of the soliton’s velocity and forcing amplitude for a given size of the circular lattice. The analysis is also reported for the circular TL including a single light- or heavymass defect. The stability chart as a whole shrinks and eventually disappears with the increase of the lattice’s size and strength of the mass defect. Qualitative explanations to these findings are proposed. We also report the dependence of the stability area on the initial position of the soliton, finding that the area is largest for some intersite position. For a pair of solitons traveling in opposite directions, there exist regimes where both solitons survive periodic collisions in small-size lattices.     

Bound soliton pulses in passively mode-locked fiber laser

A passively mode-locked soliton fiber ring laser was successfully demonstrated, and bound soliton pulses with an FWHM pulsewidth of 326 fs and fixed separation of 938 fs were first observed. The number of bound soliton pairs in the cavity can be controlled under lower pump power. The transmission effects were investigated by injecting bound soliton pulses into a single mode fiber.     

克尔介质中皮秒亮孤子多光子J-C模型粒子数反转特性

利用全量子理论研究了克尔介质中皮秒孤子光场与二能级原子多光子相互作用系统中粒子数反转随时间的变化特性,用MATLAB软件编程模拟并讨论了初始平均光子数、克尔介质与场模非线性相互作用强弱、孤子光场与原子耦合强度及相互作用过程中跃迁光子数目对粒子数反转的影响.数值计算结果表明：初始平均光子数越大、克尔介质与场模的非线性相互作用越强、孤子光场与原子耦合强度越小或相互作用过程中跃迁光子数目越多,粒子数反转崩坍与恢复的振荡幅度越小、平均值越大.     

Interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet

We study the interaction of a nonlinear spin-wave and magnetic soliton in a uniaxial anisotropic ferromagnet. By means of a reasonable assumption and a straightforward Darboux transformation one- and two-soliton solutions in a nonlinear spin-wave background are obtained analytically, and their properties are discussed in detail. On the background of a nonlinear spin-wave the amplitude of the envelope soliton has the spatial and temporal period, and soliton can be trapped only in space. The amplitude and wave number of spin-wave have the different contribution to the width, velocity, and amplitude of soliton solutions. The envelope of solution hold the shape of soliton, and the amplitude of each envelope soliton keeps invariability before and after collision which shows the elastic collision of two envelope soliton on the background of a nonlinear spin-wave.     

Dynamics of the soliton instability in the easy-plane ferromagnetic chain

We present results on the nonlinear dynamics of a realistic classical easy-plane ferromagnetic chain in an external magnetic field, concerning in particular the dependence of soliton solutions on the strength of the single-ion anisotropy. After giving two exact static solutions, slowly moving permanent profile solutions are investigated. The velocity dependent contribution to the energy as well as the amplitude of the out-of-plane distortion of these solutions is shown to diverge when the Magyari-Thomas-Kumar instability of the static Sine-Gordon soliton is approached. The dynamic origin of this instability is shown to be an unstable behaviour of the soliton towards spontaneous motion instead of a soft mode.     

深光晶格势阱中凝聚体的扭结包络隙孤子

发展准离散多尺度法结合紧束缚近似,解析地研究了局陷于光晶格势阱中凝聚体的非线性动力学性质.结果发现,系统中出现稳定的对称包络孤子外,还可观察到一种新的非线性元激发:扭结包络隙孤子.有趣的是,该隙孤子并不传播且局域在初始位置,其幅度可通过光晶格势阱的晶格常数和势阱深度来调控.相应的实验方案是:通过改变形成光晶格势阱的两交叉耦合激光束之间的夹角和(或)激光光强来调控扭结包络隙孤子的幅度.     

Resonance effects in nonlinear lattices

We study a class of one-dimensional nonlinear lattices with nearest-neighbour interactions described by a potential of the binomial type. This potential contains a free parameter which can be chosen to reproduce a variety of models, such as the Toda, the Fermi-Pasta-Ulam and the Coulomb-like lattices. Carrying out essentially numerical experiments, the effects of soliton propagation on a lattice with defects are investigated. In particular, the properties of the localized mode, generated by the propagation of the soliton through the defect, are discussed with respect to the defect mass and the potential parameter, in the light of a simple theoretical model. Furthermore, an interesting phenomenon is observed: the amplitude of the speed of the mass defect shows a sequel of resonance peaks in terms of the mass defect. The positions of these peaks appear to be independent of the potential parameter. Received 16 August 1999 and Received in final form 3 February 2000     

Temperature dependence of soliton density in the incommensurate phase of [N(CH3)4]2ZnCl4 crystals

The successive phase transitions of [N(CH₃)₄]₂ZnCl₄ have been investigated by EPR in a Mn²⁺ doped-sample. The temperature change in the resonance line shape near the commensurate-incommensurate transition temperature was analysed by a one-dimensional phase soliton model, so that the soliton density, modulation amplitude and initial phase were determined. The discommensuration phenomenon was also observed and discussed in terms of the domain wall resulting from the soliton.     

Obliquely propagating ion-acoustic solitons in a warm-ion magnetized plasma

Considering the charge separation effect, the soliton solution of the KdV equation is discussed for a warm-ion magnetized plasma with two Maxwellian electron components. The effect of ion temperature, obliqueness and magnetization on the amplitude and width of the soliton is discussed in detail. The theory is applied to the case of rarefactive solitons observed in the magnetosphere.     

Soliton pinning and the central peak

The soliton contribution to the dynamical structure factor for the one-dimensional λψ⁴ model is studied. While a soliton is pinned with some defect, the central peak width is of order of $\text{α}\text{Γ}$, where α is the impurity potential amplitude, Γ the soft mode damping rate.     

Observation of the chaotic spin-wave soliton trains in magnetic films

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.     

Dissipative longitudinal solitons in a two-dimensional strongly coupled complex (dusty) plasma

Solitary waves are experimentally studied in a monolayer hexagonal dust lattice which is formed from monodisperse plastic microspheres and levitated in the sheath of an rf discharge. It is found that the product of the soliton amplitude and the square of the soliton width is constant as the soliton propagates. The analytical theory describing the experiment is based on the equations of motion written for a linear chain. It takes into account damping, dispersion, and nonlinearity. The numerical simulation of a linear chain produces double solitons like those observed in the experiment.     

对数饱和非线性介质中的自洽多模高斯孤子解

通过解对数饱和非线性介质中光场满足的非线性薛定谔方程,得到一组厄米-高斯型的自洽多模解.在借鉴了R.G.Glauber的相干态理论的基础上,合理假设这组解在非线性介质中呈泊松分布,进而得到了在对数饱和非线性介质中存在高斯孤子的结论,并获得高斯孤子解、非线性系数与泊松参量三者之间的关系.该关系说明,若在介质中存在高斯孤子解,其非线性系数必须满足条件a≥1.当α=1,在介质中仅存在单模高斯孤子,其光斑尺寸必须满足的条件W=1/k n0/n2.在该条件下,以"束腰"注入介质中的高斯光束才可以在保持其光斑尺寸不变的情况下传输,否则光斑尺寸会存在一定的振荡.而振荡方式、振荡范围(表示光斑尺寸展宽或压缩及大小)与输入光束光斑尺寸及其一次导数有直接关系.     

Anomalous interactions of spatial gap solitons in optically induced photonic lattices

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the "staggered" phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.     

Soliton excitation in the pass band of the transmission line based on modulation

We numerically investigate the excitation of soliton waves in the nonlinear electrical transmission line formed by many cells. When the periodic driving voltage with frequency in the pass band closing to the cutoff frequency is applied to the endpoint of the whole line, the soliton wave can be generated. The numerical results show that the soliton wave generation mainly depends on the self modulation associated with the nonlinear effect. In this study, the lower subharmonic component is also observed in the frequency spectrum. To further understand this phenomenon, we study the dependence of the subharmonic power spectrum and frequency on the forcing amplitude and frequency numerically, and find that the subharmonic frequency increases with the gradual growth of the driving amplitude.     

主动锁模光纤激光器的孤子理论分析

系统考虑了光纤激光器腔构参数与锁模脉冲参数的制约关系,建立了完整形式的振幅调制主动锁模光纤激光器的稳态方程;据此方程分析了主动锁模光纤激光器腔参数对锁模孤子脉冲参数的影响;分析了无啁啾孤子脉冲形成条件。