Exploring Lump Solutions, Bifurcation, Sensitivity, and Chaotic Dynamics in the Extended KP-Boussinesq Equation

In this study, we examine several analytical rational solutions using the ansatz transformation. For the (2+1)-dimensional extended KP-Boussinesq (eKP-BO) equation, we acquire several types of lump solutions, such as lump soliton solution (LS), lump one stripe, and lump-periodic solution (LPS). Some of the produced soliton solutions are shown in 3D and 2D, and contour depictions for suitable parameter values are used to demonstrate the dependability, usefulness, and efficacy of the computational technique. Utilizing the Galilean transformation, the dynamical structure of the suggested equation is thus obtained, and the theory of the planar dynamical system is used to carry out its bifurcation. The presence of chaotic behaviors of the eKP-BO equation is examined by taking into account a perturbed term in the derived dynamical system and providing various two- and three-dimensional phase illustrations. Furthermore, the sensitivity analysis of the dynamical system confirms that minor variations to the initial conditions significantly affect the system’s behavior, demonstrating its sensitivity to initial conditions. To the best of our knowledge, this research has not been previously addressed in the literature. The outcomes are expected to be helpful to a wide range of scholars who are interested in fluid mechanics, water wave analysis, and other multidisciplinary fields.