Chaotic structures and unveiling novel insights of solutions to the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation with its stability analysis

In current research work, study the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation, which explains wave propagation in optical fibers, mathematical physics and behaviors of solitons. The results and extract using the modified Sardar sub-equation method, the analysis of phase portrait utilizing bifurcation and chaos theory. These methods have been used to extract analytical solutions for the aforementioned equation. Numerous optical solitons, such as singular solitons, solitary waves, periodic solitons, wave collisions, and phase portraits show stable and unstable nodes. The structures of the obtained results are displayed in 3-dimensional, 2-dimensional and contour plots. These solutions have extensive use in various domains, including hydrodynamics, nonlinear optics, plasma physics, fiber optics, and telecommunication systems. The dynamics of chaotic structures are displayed by choosing and appropriate parameter values. These graphs shed light on the properties and behavior of the solutions. The results collected provide evidence of the proposed method’s efficacy, dependability, and simplicity. Such mathematical tools have proved to be very effective in tackling complex challenges generated by nonlinear partial differential equations and have driven immense success in nonlinear sciences, mathematical physics, and soliton theory.