Soliton Collision in a Ferromagnetic Spin Chain Driven by a Magnetic Field

By employing an inverse-scattering transformation, the exact solution of an N-soliton train in the spin chain with a time-dependent magnetic field is derived. As a special case the one-soliton solution (N = 1) exhibits explicitly the spin precession around the magnetic field and periodic shape-variation induced by the time varying field as well. In terms of the general solution, inelastic two-soliton collision is analysed. The inelastic collision, by which we mean the soliton shape-change before and after collision, appears generally due to the time varying field.     

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.     

带弱"平台"皮秒光孤子的数值研究

通过数值求解变系数非线性薛定谔方程,发现光纤系统对带有弱“平台”的皮秒光孤子有独特的传输特性。在常参数光纤系统中,这种光孤子体现“呼吸”特性,而在特殊的分布参数光纤系统中,则能较平稳地传输。     

Generation and propagation of subpicosecond pulse train

Higher-order nonlinear Schr\"{o}dinger equation with the Hirota constraint conditions is considered, and an analytic solution, which can describe the modulational instability process, is presented. Based on the solution, a new pulse train without continuous wave (CW) background is generated in quadratures and the propagation of the pulse train is discussed in detail by simulating numerically. The results show that, unlike the propagation of the picosecond pulse train, under the effects of the higher-order terms, the pulse train cannot propagate along the fibre when the energy is very high; however, for some medium energy the pulse train can stably propagate. We also investigate the stability of the pulse train against violation of the Hirota conditions, and the results show that the pulse train can still propagate stably when the Hirota conditions are broken.     

Interactions of adjacent pulsating, erupting and creeping solitons

This paper investigates the adjacent interactions of three novel solitons for the quintic complex Ginzburg--Landau equation, which are plain pulsating, erupting and creeping solitons. It is found that different performances are presented for different solitons due to isolated regions of the parameter space where they exist. For example, plain pulsating and erupting solitons exhibit mutual annihilation during collisions with the decrease of total energy, but for creeping soliton, the two adjacent pulses present soliton fusion without any loss of energy. Otherwise, the method for restraining the interactions is also found and it can suppress interactions between these two adjacent pulses effectively.     

Theory of passively mode-locked lasers with self-frequency shift and saturable absorber response

A general theoretical model for passively mode-locked lasers is presented, in which both the self-frequency shift and either a fast or a slow saturable absorber response are taken into account. An exact soliton-like solution and condition for its existence are obtained under a definite compatible condition. The stability of the solution is analyzed by using a variational method, and a parameter region, in which the solution is linearly stable, is acquired theoretically. To verify the theoretical predictions, a typical example is given for stable pulse propagation over a long distance. The numerical results show that the soliton-like solution is stable under some perturbations within the linearly stable region and an arbitrary Gaussian pulse converges to the exact soliton-like solution after evolution in a distance.     

双环芯微结构光纤特性分析

提出了一种由硅-空气孔作包层,两个环状掺杂区作芯的双环芯微结构光纤,并用有限差分法对它进行了分析.结果表明,基模电场能由弱到强地集中在双环掺杂的芯区,且环外较弱,环心最强.在1.55 μm波段,有较大色散,这在光纤色散补偿中将起到重要作用.     

Solitons in a Heisenberg Spin Chain with an Easy Axis Under an Oscillating Magnetic Field

The Lax pair given for the equations of motion of a continuum-Heisenberg-spin chain of an easy axis in an oscillating magnetic field.Using an inverse scattering transformation we derive soliton solutions for the case of the easy axis.     

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 Schrodinger (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.     

在孤子控制下两个飞秒光孤子间的相互作用

直接运用变系数高阶非线性薛定谔方程的精确2-孤子解,来研究在孤子控制下两个飞秒光孤子间的相互作用,讨论了邻近孤子的稳定性.结果表明联合控制群速度色散分布,三阶色散分布和非线性分布能抑制两个飞秒光孤子间的相互作用,而且能避免孤子超前或滞后,在特定的孤子控制系统下,两个飞秒光孤子有良好的稳定性.