4.2. Graphical explanation of the NAEM obtained solutions
The 3D plots for the real and imaginary parts, and modulus of the solution \(Q_{1}\left(x,y=1,t\right)\) are displayed in Fig. 3(a –c) , respectively. The plots of the above solutions confirm periodic shaped solitons. Such types of behavior are ensured by their 2D cross sectional line plots at \(t=0\), as shown inFig. 3(d –f), respectively. The same tendencies have been found for the solution \(Q_{3}\left(x,y=1,t\right).\) The 3D surface plots for the real and imaginary parts of\(Q_{5}\left(x,y=1,t\right)\) are exposed in Fig. 4(a, b) , respectively, which indicate periodic solutions. However, the modulus form of \(Q_{5}\left(x,y=1,t\right)\) yields a dark soliton, which is shown in Fig. 4(c) . Such types of behavior presented byFig. (a-c) are confirmed by their 2D cross sectional line plot at \(t=0\), which are demonstrated in Fig. 4(d –f),respectively. Each of the 3D graphics of the real and imaginary parts of\(Q_{7}\left(x,y=1,t\right)\) shows a singular periodic soliton and they are illustrated in Figs. 5(a) and 5(b ), respectively. But the graphical illustration of\(\left|Q_{7}\left(x,y=1,t\right)\right|\) gives a singular type soliton only (see Fig. 5(c)) . The shaped of singular solitons are confirmed by their 2D plots, which are illustrated in Fig. 5(d–f), respectively. Moreover, the remaining obtained optical solutions via the NAEM also represent the periodic, bright, dark and singular solitons.