Families of soliton solutions and other exact solutions of the geophysical KdV model

The primary objective of the present manuscript is to investigate soliton solutions of the geophysical KdV equation. Several types of solitary-wave solutions are obtained by applying four analytical methods to the geophysical KdV equation. Such equations have applications in various scientific fields, including mathematics, physics, soliton theory, plasma physics, biology, chemistry, and nonlinear processes. The derived solutions are expressed in terms of trigonometric, hyperbolic, exponential, and rational functions. Mathematica 13.0 is employed to perform the necessary calculations and generate 2D and 3D plots to illustrate the physical behavior of the considered model. The novelty of this work lies in the construction of diverse types of exact solutions using multiple analytical methods. These results may facilitate further investigations of nonlinear models that realistically describe important physical phenomena.