Lump, lump-periodic, lump-soliton and multi soliton solutions for the potential Kadomtsev-Petviashvili type coupled system with variable coefficients.

In this article, the potential Kadomtsev-Petviashvili (pKP) type coupled system with variable coefficients is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time. In this framework, Hirota bilinear form is applied to acquire diverse types of interaction lump solutions from the foresaid equation. Abundant lump, lump-periodic, lump-soliton and multi soliton solutions to the pKP system are presented by the Hirota bilinear form and a mixture of exponentials and trigonometric functions. Lump, lump-periodic, lump-soliton and multi soliton solutions are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. The movement role of the waves is investigated, and the theoretical analysis of the acquired solutions is discussed using the bilinear technique of all produced solutions with 2D and 3D plots with respective parameters. The computational difficulties and outcomes highlight the clarity, effectiveness, and simplicity of the approaches, suggesting that these schemes can be applied to a variety of dynamic and static nonlinear equations governing evolutionary phenomena in computational physics as well as to other real-world situations and a wide range of academic fields. We used software Maple 2024 "( http://www.maplesoft.com/ )".