On some new lump, periodic and travelling wave structures to the p-generalized Burgers–Kadomtsev–Petviashvili model

The dimensionally reduced p-generalized Burgers–Kadomtsev–Petviashvili model is investigated in this paper using Hirota’s bilinear technique. The lump waves and collisions between lumps and periodic waves, the collision between lump wave and single, double-kink soliton solutions, and the collision between lump, periodic, and single, double-kink soliton solutions of the provided model are all produced. Furthermore, some new traveling wave solutions are created using the extended tanh function method. The 3D, 2D, and contour plots are used to demonstrate the nature of the nonlinear model for the appropriate set of parameters. As a result, a variety of bright, dark, periodic, rational, and elliptic function solutions are established. The applied methodologies appear to be more powerful and efficient approaches in developing some new traveling wave structures for many modern models.