Results and discussion

In this segment, a meticulous examination of evaluated results is completed with recently processed results, which highlight the distinctiveness of the ongoing review. The fact that Hosseini makes it evident [1] got the obscure and infrequent arrangements of the dispersive cubicquintic nonlinear Schrödinger equation with the aid of expansion capability technique by. Yet, in this study we have noted different arrangements in the forms of luminous, obscure, undulation, and occasional wave arrangements which introduced in various charts. On the other hand,

employing the F-extension capability technique, Naila and her coauthors [2] generated soliton and occasional single wave of nonlinear Schrödinger equation with group velocity scattering. Several of our results differ from those mentioned in [2]if we compare our achievements with their results. Nevertheless, if we attribute diverse values to the components in question, we can obtain some similar results. The arrangements evaluated in this study include dim soliton, luminous soliton, undulation solitons, mathematical arrangements, and occasional arrangements. For the features of arrangements 3D, 2D and shape and density plots of several reported arrangements are presented in Figs. (1, 2, 3, 4 and 5), by assigning appropriate parametric values. The describes the trigonometric under parametric values b₁= 1.3, b₀= 1.4, b_-1 = 1.3, 𝛽₁= 1.8, c= 1.7, 𝜇= 1.8, 𝜔= 5, 𝛼₂= 1.8, 𝛼₁= 1.6, 𝛼₃= 1.3, 𝛽₂= 1.6, k= 6 and − 4≤ z _≤ 4, − 4≤ t _≤ 4. The Fig. (1) signifies the periodic solutions under parametric values b₁= 0.30, _b₀= 1.2, _b₋1 = 1.3, 𝛽₁= 1.05;_c= 1.73;𝜇= 1.8;𝜔= 3;𝛼₂= 1.7;𝛼₁= 1.5;𝛼₃= 1.25;𝛽₂= 1.55;k= 6;

Figure 1 Graphical interpretation for ^u₂(^z,t)

Figure 2 Graphical interpretation for ^u₁(^x,t)

and − 4≤ z ≤ 4, − 4≤ t ≤ 4 which. The Fig. (2) demonstrated the luminous soliton under parametric values 𝛽 = 0.8, 𝛼 = 0.67, 𝛾 = 0.5, b1 = 0.8, a1 = 0.9, 𝜔= 0.45, b−1 = 0.95, b0 = 0.55, 𝜆= 0.96 and − 4≤x≤ 4, − 4 ≤ t ≤ 4. The Fig. (4) demonstrates crimp arrangement under parametric values 𝛽 = 0.8, 𝛼 = 0.06, 𝛾 = 0.05, b1 = 1.25, a1 = 0.9, b−1 = 0.35, 𝜆= 0.45, 𝜔= 0.78, a0 = 0.55, b0 = 0.65 and − 4≤x≤ 4, − 4≤ t ≤ 4. The Fig. (4) connotes the dim soliton arrangement under parametric values 𝛽 = 0.28, 𝛼 = 0.3, 𝛾 = 0.25, b1 = 1.45, a1 = 0.98, b−1 = 0.55, 𝜆= 0.55, 𝜔= 0.88, a0 = 0.65, b0 = 0.75, a−1 = 0.2 and − 4≤x≤ 4, − 4≤ t ≤ 4. These detailed arrangements have some actual significance for example dim soliton depicts the singular waves with lower power than the background. Dim solitons are more challenging to handle than standard solitons, yet they have proved to be more stable and resilient to losses. Undulation waves are traveling waves, which ascend or descend from one asymptotic state to another. The Crimp arrangement approaches a constant at infinity. Periodic wave arrangement depicts a wave with repeating continuous pattern, which determines its frequency and period defines as time needed to complete one cycle of waveform and frequency is numerous cycles per second of time.