Assorted soliton solutions to the nonlinear dispersive wave models in inhomogeneous media

The Sharma-Tasso-Olver and Klein-Gordon equations are significant models to interpret plasma physics, relativistic physics, quantum mechanics, nonlinear optics, etc. In the present article, an advanced generalized approach, namely the generalized (G '/G)-expansion approach is scheduled to unfold certain wave solutions to the nonlinear evolution equations earlier described. The soliton solutions exposed are estimated in the form of hyperbolic, rational and trigonometric functions. The physical implications of the ascertained solutions are summed up by setting specific values of the integrated constraints and delineating the profiles to decode the physical phenomena. The numerical simulation of the solutions extracted is standard kink, rogue wave, brightdark soliton, periodic soliton, breather type soliton, compaction, singular kink soliton, etc. This study affirms that the introduced scheme is robust, efficient in searching for nonlinear evolution equations, computer algebra compatible, and capable of finding further inclusive wave solutions.