New analytical solutions of the \((3+1)\)-dimensional generalised B-type Kadomtsev–Petviashvili equation

Genralised B-type Kadomtsev–Petviashvili (gBKP) equation corresponds to the weak dispersive nature of the propagating waves in quasi-media and fluid mechanics. In this paper, a collection of exact soliton and periodic wave solutions are obtained for the (\(3 + 1\))-dimensional gBKP equation using the well-known generalised exponential rational function (GERF) method. Several classes of exact soliton and periodic solutions are derived using trigonometric and hyperbolic functions by employing this method. A graphical representation of the solutions is also presented to analyse the dynamics of the system. With the help of the computational software Mathematica, the visualisations for the wave configuration of various solutions are presented using three- and two-dimensional plots. The plots represents the wave profile of a wide range of singular soliton, multi-solitons and periodic solitons obtained for the considered equations by taking appropriate values for the associated parameters. The collection of solutions listed in the article signify the importance and possible application of GERF method to a wide variety of nonlinear differential equations in physical phenomena.