The propagation of hyper-geometric optical soliton waves in plasma dynamics for the integrable Zhanbota-IIA equation

This research utilizes the new auxiliary equation method to investigate solitary wave patterns in the integrable Zhanbota-IIA equation, a model relevant to phenomena like tidal waves and tsunamis. This method simplifies complex nonlinear-coupled partial differential equations into ordinary differential equation through a traveling wave transformation. Previous studies have not achieved such solutions. The main aim is to enhance comprehension of the integrable Zhanbota-IIA equation behavior under various conditions. Prior to this study, there does not exist any study in which such kinds of solutions are discussed by using the new auxiliary equation method. The new auxiliary equation method is utilized to derive analytical solutions for the underlying model equation. These solutions are expressed in the form of hyperbolic, trigonometric, exponential, and rational functions such as dark, bright, periodic, dark–bright, smooth topological with high peaks, dark-singular, bright singular and periodic singular. The key advantage of this method compared to others lies in its capacity to yield more comprehensive solutions with certain flexible parameters. To illustrate the dynamic structures of these solutions, 3D and 2D graphs are employed with suitable parameter values. This study explores soliton behavior and its telecommunication applications, integrating mathematics, computer science, and physics for technological advancements.