Dynamics of vector solitons in two-component Bose--Einstein condensates with time-dependent interactions and harmonic potential

We present two kinds of exact vector-soliton solutions for coupled nonlinear Schr?dinger equations with time-varying interactions and time-varying harmonic potential. Using the variational approach, we investigate the dynamics of the vector solitons. It is found that the two bright solitons oscillate about slightly and pass through each other around the equilibration state which means that they are stable under our model. At the same time, we obtain the opposite situation for dark--dark solitons.     

Stability of Bright Solitons in Bose-Einstein Condensates

We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Oross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.     

Exact Nonstationary Solutions of a Two-Component Bose-Einstein Condensate

We investigate the exact nonstationary solutions of a two-component Bose Einstein condensate which compose of two species having different atomic masses. We also consider the interesting behavior of the atomic velocity and the flow density. It is shown that the motion of the two components can be controlled by the experimental parameters.     

Dissipation-Managed Bright Soliton in a 1D Bose-Einstein Condensate in an Optical-Lattice Potential

We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-onedimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we demonstrate that the height （as well as width） of bright soliton may have little change through selecting experimental parameters.     

Interactions between Components of Various Vector Solitons in Bose-Einstein Condensates

We investigate the interactions between components of various vector solitons in Bos-Einstein condensates by means of the least action principle, and derive the effective potentials for different vector solitons, which indicate that the interactions are of short range, and may be repulsive or attractive decided by the different intra- and inter-species interactions in such a system. In the case of attraction, the two solitons will oscillate about and pass through each other around the equilibrium state. The comparison of analytical results with mumertical simulation is presented.     

亮孤子微扰论的一种直接方法

发展了一种基于分离变量法的非线性Schordinger方程的微扰论直接法。导出了微扰对亮孤子的一阶效应,即导出了孤子参数随时间的缓慢变化及微扰对孤子的一阶修正     

KdV孤子的含时微扰理论

研究了周期性含时微扰对KdV(Korteweg de Vries)孤子的影响. 将微扰项展为时间变量的傅里叶级数,发现其常数项是导致长期项的根源. 在一阶近似下,消除长期项,求出了孤子参数(高度、宽度和速度)随时间的缓慢变化. 傅氏级数中的其他项决定了微扰对孤子波形的一阶修正. 关键词： KdV孤子 孤子微扰论     

Propagation of bright femtosecond pulses in a nonlinear optical fibre with the third- and fourth-order dispersions

We solve the generalized nonlinear Schr\"{o}dinger equation describing the propagation of femtosecond pulses in a nonlinear optical fibre with higher-order dispersions by using the direct approach to perturbation for bright solitons, and discuss the combined effects of the third- and fourth-order dispersions on velocity, temporal intensity distribution and peak intensity of femtosecond pulses. It is noticeable that the combined effects of the third- and fourth-order dispersions on an initial propagated soliton can partially compensate each other, which seems to be significant for the stability controlling of soliton propagation features.