Dynamics of various solitonic formations and other solitons of a (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation using a newly designed analytical method

In this paper, we use a newly formed generalized exponential differential rational function (GEDRF) method to show the dynamic patterns of closed-form analytical solutions to the (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) equation. To help comprehend these solutions, we have also provided extensive three-dimensional and contour illustrations that show their distinctive characteristics such as lump forms, soliton forms, and interactions between solitons and newly formed waves. These visual representations enhance the comprehension of the solutions behaviors and properties. The derived generalized soliton solutions have extensive applications across various domains: in oceanography for modeling wave dynamics, in physics for studying wave propagation in different media, in engineering for the development of wave-related technologies, and in nonlinear dynamics for theoretical advancements. We used MATHEMATICA to show the multiple dynamic formations of soliton solutions, such as multi-peakons, multi-lumps, and interactions between them, which have been generated with various parameter values using numerical simulations and symbolic computations. Solitons can be found in a wide range of fields, including plasma physics, oceanography, and optical fibers. These findings highlight the versatility and significance of the DSKP equation within various scientific and related technology areas.