Study of soliton solutions, bifurcation, and sensitivity analysis in the Davey–Stewartson–Kadomtsev–Petviashvili model

This study investigates lump soliton solutions, bifurcation behavior, and sensitivity analysis of the ([Formula: see text])-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) model. We use Hirota bilinear technique (HBT) to construct new lump soliton solutions such as U-shaped, S-shaped, and line-shaped forms with a time-varying amplitude parameter, [Formula: see text]. Additionally, we present a complete bifurcation analysis and sensitivity estimation by creating an associated dynamical system for the DSKP equation through the Galilean transformation (GT). Our study reveals abundant nonlinear behaviors, stability properties, and parameter-dependent phase portraits via analytical and numerical methods. The examination is further enhanced by the inclusion of comprehensive two- and three-dimensional phase portraits that provide visual insight into the system’s dynamic behavior. The findings significantly enrich our understanding of nonlinear wave phenomena and provide insightful information on potential applications in coastal engineering, plasma physics, and fluid dynamics.