Figure 1

Multifaceted graphical illustrations, encompassing 3D surface plots, 2D profiles, and contour maps, providing insights into the bright solitary wave solutions derived from the analytical techniques, given by Eqs. (5) (a–c), (7) (d–f), and (9) (g–i). The visualizations enable enhanced examination of the waveform amplitude, localization, propagation, and spatial evolution characteristics.