Formation mechanism of asymmetric breather and rogue waves in pair-transition-coupled nonlinear Schrödinger equations<xref rid="cpb_28_1_010504fn1" ref-type="fn">*</xref> <fn id="cpb_28_1_010504fn1"> <label>*</label> <p>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).</p> </fn>

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-Dong^{1, 2, †}, Wang Yang-yang¹, He Peng-Bin³

A sketched demonstration of the density plot in the limit \ | ν | → ( a 1 2 + a 2 2 ) − in Akhmediev breather solution using Eq. (6) with C₁ = −1, C₂ = 1, C₃ = 3, C₄ = −3, a₁ = 0.8, and a₂ = 0.7. Note that there is one peak and two caves in each periodic. (a)–(c) Density plots for component |q₁|², and (d)–(f) density plots for component |q₂|². The modulation parameter ν of the Akhmediev breather is as follows: (a) and (d) ν = 0.7746; (b) and (e) ν = 1; (c) and (f) ν = 1.063.