Diverse analytical wave solutions of plasma physics and water wave equations

Abstract

In plasma physics and water waves, the Gilson-Pickering equation is an important unidirectional wave propagation model. A large number of analytic wave solutions have been established in the form of hyperbolic, trigonometric, exponential, and rational functions using the advanced auxiliary equation approach in this study. The solutions obtained have been compared with the solutions available in the literature, and it is observed that we have established further wave solutions than the solutions determined by the other methods, namely the (G′/G2)-expansion method, sinh-Gordon approach, etc. This method uses a homogeneous balance rule to estimate a polynomial-type solution and delivers an order. A traveling wave transformation has been used to convert the governing equation into a nonlinear differential equation. Each solution includes a variety of parameters related to the model and method. Using different parameter values, the nature of wave solutions is defined by three-dimensional (3D) and two-dimensional (2D) wave profiles. The solitons change their nature and location for the particular values of the dispersion coefficient α and free parameter κ, and shown in 2D figures to illustrate the different forms of solitons.