Examine the soliton solutions and characteristics analysis of the nonlinear evolution equations

The consistent and feasible enhanced (G '/G) -expansion technique is applied to construct an assortment of fresh and universal soliton solutions to the two important nonlinear evolution equations. One of them is the Benjamin-Ono equation, which is a partial differential equation that describes the propagation of weakly nonlinear and weakly dispersive long waves in deep stratified fluids in one dimension. Another equation is the modified Benjamin-Bona-Mahony equation, which is a variant of the Benjamin-Bona-Mahony equation and is used to examine Rossby waves in rotating fluids as well as drift waves in plasma. In this study, we investigated the aforementioned equations and obtained sufficient soliton solutions, such as bell soliton, periodic and kink-shape soliton, singular and singular-kink soliton, and so on. All the solutions achieved have physical explanations, and plotting some 3D figures reveals the diverse physical configurations and characteristics. We also include a comparison of other's solutions in the literature to our own, which validates our solutions. The solutions indicate that the mentioned method is adaptable, improved, and effective for other nonlinear evolution equations in mathematical physics.