Chirped soliton-like solutions for nonlinear Schrödinger equation with variable coefficients

The exact chirped bright and dark soliton-like solutions of generalized nonlinear Schrödinger equation including linear and nonlinear gain(loss) with variable coefficients describing dispersion-management or soliton control is obtained detailedly in this paper. To begin our numerical studies of the stability of the solutions, we present a periodically distributed dispersion management or soliton control system as an example. It is found that both the bright and dark soliton-like solutions are stable during propagation in the given system. The numerical results are well in accordance with those obtained by analytical methods.     

Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length

A parabolic index dispersion decreasing fiber (DDF) has been designed and optimized to produce high capacity soliton communication system. Variation of different fiber parameters such as core radius, effective core area and GVD factor along the 25 km of DDF length has been carried out to optimize a best possible DDF which can sustain the propagation of fundamental soliton. The variation of non-linearity with length along with the conventional power and GVD factor variation has been included in the generalized non-linear Schrodinger equation (NLSE). This NLSE has been solved numerically by split step Fourier method for shorter pulse propagation, incorporating the term for third order dispersion and intrapulse Raman scattering. Stable soliton pulses in transmission system have been achieved by our simulation, when a correction factor due to Raman induced soliton mean frequency shift is incorporated to the GVD profile predicted by the fundamental soliton condition. The interaction of neighboring soliton pulse pair through the proposed fiber has also been studied.     

Topological and dynamical excitations in a classical 2D easy-axis Heisenberg model

The properties of dynamical solitons (magnon droplets) in the classical, two-dimensional anisotropic Heisenberg model with easy-axis exchange anisotropy are studied. The solution of the Landau-Lifshitz equation in the continuum limit for the soliton with topological charge q = 1 is obtained numerically using a shooting method. We analized a wide range of the anisotropy parameter and our results are in good agreement with results obtained from spin dynamics simulations. The dependence of an internal precession frequency of the soliton on both the anisotropy parameter and the radius of the soliton is also investigated. Finally, the limits of applicability of the continuum approach are discussed. Received 22 August 2000     

Effects of dark soliton crystal temperature on the self-deflection of bright soliton in a biased serial photovoltaic photorefractive crystal circuit

Based on the theory of one-dimensional separate soliton pairs formed in a serial photovoltaic photorefractive crystal circuit, the effects of the dark soliton crystal temperature on the self-deflection of the bright one in a bright-dark soliton pair are investigated. The numerical results indicate that the spatial shift of the bright soliton can experience obvious increase in their self-deflection with the increase of the temperature of the dark soliton. The self-bending process is further studied using perturbation techniques and the results are found to be good agreement with that obtained by numerical method.     

Optical beams in lossy non-local Kerr media

It is discussed that optical beams propagate in non-local Kerr medium waveguides with losses. A variational principle is carried out for the 1 + 1-D non-local non-linear Schrödinger equation in the presence of the losses. In the strongly non-local case, the approximate analytical solutions are obtained. The lossy soliton solution shows that, Unlike its local counterpart, such lossy strongly non-local soliton does not possess the adiabatic property anymore. In addition, the general approximate results for non-soliton cases are gained. The comparisons between our approximate analytic solutions and numerical simulations confirm our variational approximate solutions.     

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.     

Two velocity difference model for a car following theory

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model.     

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schrödinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.     

在采用集总放大器的光孤子优越传输中啁啾的作用

讨论了光孤子传输中，由脉冲包络的相位变化产生的啁啾与孤子传输的关系。数值计算表明，当孤子脉冲收缩、展宽时，啁啾总是改变符号，利用啁啾也可以定出孤子传输的光纤临界长度（即孤子传输中集总放大器的间隔），其效果比用脉宽恢复定出的临界长度要好     

Variational analysis of evolution for magnetostatic envelope bright soliton with higher-order dispersion

The evolution characteristics of a magnetostatic envelope bright soliton in magnetic thin films with higher-order dispersion are investigated analytically by means of the variational approach. It is found that the envelope of the soliton is changed due to the effects of the higher-order dispersion; the evolution of the soliton does not depend on its phase; and a stationary soliton can be formed in an appropriate situation. It reveals the relation between the motion of the soliton and the initial input pulse area.     

Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect

We report the quantized superfluid vortex filaments induced by the axial flow effect, which exhibit intriguing loop structures on helical vortexes. Such new vortex filaments correspond to a series of soliton excitations including the multipeak soliton, W-shaped soliton, and anti-dark soliton, which have no analogue when the axial flow effect is absent. In particular, we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex, while the vortex filament induced by the anti-dark soliton is caused only by the bending action, which is consistent with the case of the standard bright soliton. These results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices.     

Weierstrass \wp -lumps

We present our results of a numerical investigation of the behaviour of a system of two solitons in the (2+1) dimensional CP¹ model on a torus. Defined by the elliptic function of Weierstrass, and working in the Skyrme version of the model, the soliton lumps exhibit splitting, scattering at right angles and motion reversal in the various configurations considered. The work is restricted to systems with no initial velocity. Received 24 April 2001     

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。     

Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Interactions of solitons with complex defects in Bragg gratings

We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons.     

New properties of magnon density in uniaxial anisotropic ferromagnet on the background of spin wave

The N-soliton solutions of magnetization in uniaxial anisotropic ferromagnet on the background of spin wave are presented by using the effective Darboux transformation method. With the analytical solutions new properties of magnon density is studied in detail. On the ground state background the magnon density is constant for the spin wave solution and the magnetic soliton, respectively. However, on the spin wave background the magnon density possesses of temporal or spatial periodic oscillation. Moreover, the soliton solution possess the breather character in its propagation along the ferromagnet. These results show that during soliton propagation a periodic magnon exchange occurs between the magnetic soliton and the spin wave background.     

Regimes of operation states in passively mode-locked fiber soliton ring laser

The principal of passively mode-locked fiber soliton ring lasers is summarized, including its three output operation states: normal soliton, bound–solitons and noise-like pulse. The experimental results of the passively mode-locked fiber soliton ring lasers developed by us are given. Bound–solitons with different discrete separations and three-bound–solitons state have been observed in our fiber laser for the first time. The relationship among three operation states in fiber soliton laser is analyzed.     

Femtosecond soliton generation induced by intrapulse stimulated Raman scattering in optical fibers

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ABUNDANT DROMION-LIKE STRUCTURES TO THE (2+1) DIMENSIONAL KdV EQUATION

The abundant generalized dromion structures for the (2+1)-dimensional KdV equation are obtained using the homogeneous balance method. We give not only the general curve soliton which is finite on a curved line and localized apart from the curve, find but also the dromion solutions which can be driven by two perpendicular line soliton and by two non-perpendicular line soliton and by one line soliton and one curve line soliton. Various types of multi-dromion solutions can be constituted by selecting different arbitrary functions of y. The (1+N) dromion obtained by Radha et al.^[3] is only a very special case of our results.