This study examines the 1 + 2 -dimensional Zoomeron equation, which has recently become popular in applied mathematics and physics. Bright soliton (non-topological), kink wave solution and traveling wave solutions are generated with the advantages of the generalized exponential rational function method. With the help of this method, it is aimed to produce different types of solutions for the Zoomeron equation compared to other traditional exponential function methods. The effects of parameters on the amplitude of the wave function are discussed, along with physical explanations backed by simulations. In addition, the advantages and disadvantages of the method for the 1 + 2 -dimensional Zoomeron equation are discussed.

This study emphasizes the importance of understanding natural phenomena through various observations and relating them to scientific studies. Nonlinear partial differential equations serve as fundamental tools for modeling these phenomena, with a focus on nonlinear evolution equations when involving time. This paper investigates the dynamics of the Zoomeron equation, highlighting not only a result derived from the KdV and Schrödinger equations but also its contribution to the modeling of Boomeron and Trappon solitons. Different analytical techniques yield various solutions for the Zoomeron equation, each offering unique insights. The behavior of the solutions generated in kink and singular soliton forms in various dynamics using the G ′ / G 2 -expansion method is investigated and compared under restrictive conditions, and the distribution of energy density is explained with the assistance of the gradient function. It is aimed at gaining a physically unique perspective by revealing the connections between the velocities of solitons produced for this equation and the effects of gradient flow directions. In addition, stability analysis for some of the solutions generated in the kink form is investigated. The structure of the paper includes method introduction, application, stability property, results and discussion, resulting in a unique perspective on understanding the physical dynamics of the Zoomeron model.