Soliton Solutions and Other Solutions to the (4+1)-Dimensional Davey–Stewartson–Kadomtsev–Petviashvili Equation using Modified Extended Mapping Method

Our goal in this paper is to obtain the travelling wave solutions of the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation (DSKPE), which considered as a fundamental tool in studying a variety of phenomena appear in many applications of fluid mechanics and ocean engineering. This equation is used to describe the non-elastic and elastic interactions between internal waves. The novelty of this equation is due to the involvement of complex time which further holds importance within the theory of advanced modern nonlinearity. Our Study mainly depend on applying the modified extended mapping method to get the solitary wave solutions and other exact solutions of our model of interest. Many classification of solutions are established like (bright, dark, singular, combo dark-singular) soliton, also hyperbolic wave solution, as well as periodic, singular periodic, exponential and rational solutions. The three-dimensional and contour plots are depicted for some selected solutions to show the dynamics of the extracted solutions.