Exact soliton solutions for the (n + 1)-dimensional generalized Kadomtsev–Petviashvili equation via two novel methods

In this study, we deal with the [Formula: see text]-dimensional generalized Kadomtsev–Petviashvili equation (gKPE). This equation is an extension of the classical KP equation to higher dimensions, allowing for the study of nonlinear wave propagation in [Formula: see text] dimensions. Like the original KP equation, the [Formula: see text]-dimensional version can support soliton solutions, which are stable waveforms that retain their shape while traveling. The [Formula: see text]-dimensional gKPE has several applications in different physical systems, such as optical fibers, Bose–Einstein condensates, fluid physics, and plasma physics. We use two efficient methods to search for analytical solutions to the equation we consider. One of these methods is the generalized unified method and the improved [Formula: see text]-expansion method. Using these techniques, we obtain many soliton solutions of rational, hyperbolic, and trigonometric types. We present 3D, contour, and density plots to observe the behavior of some of the solutions we obtained. The acquired results constitute an essential resource for the study of hydrodynamic waves, plasma fluctuations, and optical solitons and offer useful information for understanding the behavior of the KPE under different physical situations. The methodologies used in this study are robust, influential, and practicable for diverse nonlinear partial differential equations; to our knowledge, these methods of investigation have not been explored before for this equation. The accuracy of each solution has been verified using the Maple software program.