Fig. 1. The asymptotic processes of the magnetic component in the limit processes and in Eq. (3), where the parameters are as follows: A_s = 0.9, k_s = 1: (a) μ = 0.82; (b) μ = 0.89; (c) μ = 0.89999; (d) μ = 1.1; (e) μ = 0.96; (f) μ = 0.9001, respectively. 方程(3)在 的极限条件下, 磁化分量 的渐近过程, 参数如下: A_s = 0.9, k_s = 1　(a) μ = 0.82; (b) μ = 0.89; (c) μ = 0.89999; (d) μ = 1.1; (e) μ = 0.96; (f) μ = 0.9001

Fig. 2. The graphical evolution of rogue waves for the magnetization in Eq. (3) and (7), i.e., bright rogue waves (a)−(c) and dark rogue waves (d)−(f). The parameters are as follows: , and with the sign corresponding to the bright and dark rogue waves, respectively^[54]. 方程(3)和(7)中磁化强度 的怪波演化图, 即(a)−(c)为亮怪波, (d)−(f)为暗怪波. 参数: , ±分别表示亮怪波和暗怪波^[54]

Fig. 3. The formation of magnetic petal in the component of Eq.(3) under the special condition of A_s = 1, . The parameters are as follows: . 方程(3)在A_s = 1, 的条件下, 磁化分量 四片花瓣结构的演化图. 参数如下: A_s = 1,

Fig. 4. The magnon density distribution against the background for the different parameter , which ranges from 0.09 to 0.29 in 0.05 steps^[53]. The inset figure is the magnon density distribution against the background for the excited formation of magnetic rogue wave. Other parameters are . 不同的参数 下的磁振子密度分布图^[53], 范围从0.09到0.29间隔0.05. 插图为怪波形成时的磁振子密度. 其余参数为

Fig. 5. (a)−(e) The formation region in space for magnetic rogue wave with different current^[53]. The parameter ranges form 0 to 0.8 in 0.2 steps; (f) The nonuniform exchange of magnons between rogue wave and background for the different spin current. The inset figure in (f) denotes the maximal accumulation (or dissipation) process for the critical current value . Other parameters are . (a)−(e)不同电流值激发怪波在区域 的分布图^[53], 电流从0到0.8, 间隔为0.2; (f)不同电流怪波形成时的图形, 插图为磁振子积聚的最大时情况. 临界电流 , 其它参数