A comprehensive study of solitons and chaotic dynamics in the (3+1)-dimensional extended Kadomtsev-Petviashvili equation

This paper studies the analytical and dynamical behavior of a generalized (3+1)-dimensional extended Kadomtsev-Petviashvili (eKP) equation, which includes higher-order nonlinear and dispersive effects. Using the exp $(-\phi (\xi ))$-expansion method, exact traveling wave solutions are obtained successfully. The solutions exhibit rich nonlinear wave structures, including localized solitons, periodic waves, and breathing patterns. To further explore the qualitative behavior of the system, a reduction of traveling waves is used, resulting in a planar dynamical system. A bifurcation analysis is carried out in detail by investigating the equilibrium points, Jacobian structures, and their relations to system parameters. The phase portraits show topological transitions such as centers, saddles, and cusp points. Moreover, a perturbed form of the reduced system is considered in order to investigate chaotic dynamics under periodic external forcing. The existence of chaos is verified using bifurcation diagrams, sensitivity analysis, Poincaré maps, time series, and both 2D and 3D phase portraits. These numerical simulations confirm the theoretical predictions and demonstrate the system's complex behavior across varying perturbation parameters. Overall, the outcomes provide a complete picture of the soliton structures and chaotic regimes that the eKP model may exhibit in physico-nonlinear wave propagation in multidimensional contexts.