Dynamical analysis and extraction of solitonic structures of a novel model in shallow water waves

In this study, we utilized a novel auto-Bäcklund transformation and the extended transformed rational function approach to analyze the extended reduced Jimbo–Miwa equation, a prominent equation within the KP hierarchy. The homogenous balance technique was employed to derive the auto-Bäcklund transformation of the equation, leading to the extraction of new exact solutions exhibiting solitary patterns. Additionally, we applied the extended transformed rational function method, which relies on the Hirota bilinear form of the governing equation, to generate complexiton solutions. Furthermore, we included 3D graphics visualizing the obtained solutions.