The phase transition regions of nonlinear modes as the function of the amplitude and width of the initial pulse are shown in figure
2(a) when
C = 0, and the phase transition region of rogue wave is shown in figure
2(b) when
C = 1. We choose some points (black points 1–6 in figure
2(a) and black points 1–2 in figure
2(b)) to exhibit their propagating results. Here, the corresponding nonlinear modes are shown in figures
2(a1)–(a6), and (b1)–(b2). We introduce the full width at half maximum (FWHM) of nonlinear modes
W to denote their distribution regions. For the SNLSE, FWHM of figures
2(a1)–(a6) are
W = 1.02, 1.10, 1.17, 1.33, 1.64, and 0.86, respectively, and the one of figure
2(b1) is
W = 1.25. According to the above criterions about nonlinear modes, we find the yellow regions located by the black point 1 are for rogue waves, the regions located by the black point 2 are the transition regions of rogue waves and breathers, the blue regions located by the black point 3 are the breathers, the regions located by the black point 4 are the transition regions of breathers and solitons, the red regions located by the black point 5 are the solitons, and there is not the soliton solutions in the regions located by the black point 6. In figure
2(b), the regions located by the black point 1 denote the existence interval of rogue waves as shown in figure
2(b1) when the nonlinear coefficient
σ1 = −9.6 and −4.8. It is obvious that the existence regions of rogue waves are effected by the nonlinear coefficient
σ1.