Stability analysis, $$\:{\varvec{\phi\:}}^{6}$$ model expansion method, and diverse chaos-detecting tools for the DSKP model

This paper talks about the [Formula: see text]-model expansion method for the Davey-Stewartson- Kadomtsev-Petviashvili (DSKP) model in (4 + 1) dimensions. This is useful for studying shallow-water waves, coastal engineering, fluid mechanics, and plasma physics. We use a variable relation to transform the model's partial differential form into an ordinary one. Computational software then examines the resultant model using the previously outlined methods. Combining solutions for Jacobi elliptic, hyperbolic, and trigonometric forms yields novel dynamical optical solitons. We also employ a planar dynamical process to examine the governing model qualitatively. We also investigate stability analysis, bifurcation, and chaotic behavior with diverse chaos-identification tools. The study's findings allow us to conclude that the approach is favorable, helpful, soothing, and suitable for handling a variety of nonlinear models.