Lump, breather, and multi-wave solutions of an extended (3+1)-dimensional generalized Kadomtsev-Petviashivli equation

The presented paper discusses an extended (3+1)-dimensional generalized Kadomtsev-Petviashivli equation through the use of the Hirota bilinear method and the modified extended tanh method. Bilinear equations are derived using Hirota’s derivatives, which will result in the derivation of lump, breather, two-wave, and three-wave solutions. The obtained solutions have applications in fluid dynamics and are pertinent to the focus on wave and charged particle interactions in plasmas. Furthermore, the modified extended tanh method is applied to derive a solution, yielding hyperbolic, trigonometric, and rational solutions with adjustable parameters. The obtained results demonstrate the practicality, simplicity, and effectiveness of the proposed methods in wave characterization behaviors, and novel wave strategies are being introduced for a range of nonlinear equations encountered in the engineering field. The visualization of our solution is further enhanced by 3D and 2D graphs.