<p>In this study, the improved generalized Riccati equation mapping method is applied to the Zhanbota-IIA equation to get analytical solutions. Through this application, we construct various types of optical soliton wave solutions. They are rational, exponential, trigonometric, and hyperbolic function solutions. The results obtained are verified for accuracy and consistency through symbolic computation using Maple software. After the mathematical study, we graphically present some solutions in several dimensions such as, two-dimensional, three dimensional and contours to examine the physical characteristics and structural that comprise kink, dark, bright, and rogue waves from some selected solutions. The findings of the study shows that the method is efficient and beneficial for tacking of complex nonlinear equations arising soliton dynamics in nonlinear science.</p>