Bifurcations, chaotic behavior, sensitivity analysis and soliton solutions of the extended Kadometsev–Petviashvili equation.

The main aim of this study is to conduct an in-depth exploration of a recently introduced extended variant of the Kadomtsev–Petviashvili (KP) equation. To achieve this goal, we employ the Galilean transformation to derive the dynamic framework associated with the governing equation. Subsequently, we apply the principles of planar dynamical system theory to perform a bifurcation analysis. By incorporating a perturbed element into the established dynamic framework, we explore the potential emergence of chaotic behaviors within the extended KP equation. This investigation is supported by the presentation of phase portraits in both two and three dimensions. Additionally, to ascertain the stability of solutions, we conduct a sensitivity analysis on the dynamic framework employing the Runge–Kutta method. Our results affirm that minor variations in initial conditions have minimal impact on solution stability. Furthermore, employing the modified tanh method, we construct multiple instances of solitons and kinks for the proposed model. [ABSTRACT FROM AUTHOR]