Dynamical aspects and qualitative analysis related to an extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation

Shallow water waves in coastal regions are commonly described by nonlinear partial differential equations. In this study, a new extended (3+1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated to model the propagation of shallow water waves. A Galilean transformation is employed to reduce the model to a planar dynamical system, followed by bifurcation and dynamical analyses. Standard detection tools such as phase portraits, Poincaré sections and Lyapunov exponents are applied to the perturbed system showing that the perturbed dynamics remain quasi-periodic for the given conditions rather than chaotic. The sensitivity of the system is examined using three distinct initial conditions. Then, Hirota's bilinear form is applied to derive exact wave solutions which are highlighted through 3D surface and density plots. These results provide new insights into the nonlinear dynamics and wave propagation characteristics of the proposed model.