Fig. 1. (a) and (b) show the and change with for ; (c) and (d) display and change with for ; (e) shows the critical value versus for . (a)，(b) 时固定点解 和 随线性塞曼劈裂 的变化; (c)，(d) 时固定点解 和 随线性塞曼劈裂 的变化; (e) 时临界值 随 的变化

Fig. 2. (a), (b) show the comparisons between the variationally predicted stationary soliton solutions (circles) and the numerical solutions (solid lines) of stationary solitons of GP equation (2) for and with , respectively. The other parameters are and ；(c)−(f) are the dynamical evolutions of solitons in time-dependent GP simulations by using the variationally predicted stationary soliton solutions in (a) and (b) as initial wave functions, respectively (a)和(b)分别展示 和 时, 变分静态孤子解(圆圈)与GP方程（2）静态孤子的数值解(实线)的对比, 其他参数取值为 , 及 ; (c)—(f)分别为(a)和(b)中的变分静态孤子解作为初始条件在含时GP方程中的动力学演化

Fig. 3. The frequency changes with for and in (a) and (b), respectively. (a)和 (b)时, 频率 随线性塞曼劈裂强度 的变化

Fig. 4. (a)−(f) show the dynamical evolutions of initially balanced solitons with , and in GP simulations, in (a)−(c), and in (d)−(f); oscillation period and moving velocity of solitons change with the linear Zeeman splitting. (a)—(f)初始值为 , 及 的孤子动力学演化　(a)—(c) , (d)—(f) ; 孤子振荡周期 及速度 随线性塞曼劈裂的变化