Abstract
This paper investigates the soliton wave on a free-moving fluid surface by studying the two-fluid model, which are the fourth-order Boussinesq and the modified Liouville equation. This study depends on one of the computational schemes to find exact and soliton wave solutions of these models. These solutions give novel physical properties of these waves, which enable their use in many fluid applications. In order to achieve our goal, the exp(+/-Phi(xi))-expansion method is applied to these two models, and for more explanation of the physical properties of these models, some of the obtained solutions are sketched in different forms (two, three-dimensional and contour plots). Moreover, the obtained results are discussed for its novelty and how it changed from that achieved in the previous work.