Formation mechanism of asymmetric breather and rogue waves in pair-transition-coupled nonlinear Schrödinger equations*

Project supported by the National Natural Science Foundation of China (Grant No. 61774001) and the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ2045).
Li Zai-Dong1, 2, †, Wang Yang-yang1, He Peng-Bin3
       

Density plots of the Kuznetsov–Ma breather solution in Eq. (6) with specific values of ν = 1, C1 = 1, C2 = 0, C3 = 3, and C4 = 2. The white boxes in the figure represent a period, as in the figures below. (a)–(c) Plots for the component |q1|2 and (d)–(f) plots for the component |q2|2. From each time period unit, it is seen that (a) has one peak and two valleys, and (d) has only one peak. Other parameters are as follows: (a) and (d) a1 = 0.59, a2 = 0; (b) and (e) a1 = 0, a2 = 0.7055; (c) and (f) a1 = 0.59, a2 = 0.7055.