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 āc) , 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 āf), 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 āf),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(dāf),
respectively. Moreover, the remaining obtained optical solutions via the
NAEM also represent the periodic, bright, dark and singular solitons.