Applications of the tan(𝑭(𝝃)/𝟐)-expansion method to the nonlinear partial differential equations

This work is made up of the five sections. In section one, we describe and show some basic definitions that are must be in this study. In section two, we going to show the general structures of the (𝑭(𝝃)/𝟐)-expansion method. In section three, we apply the(𝑭(𝝃)/𝟐)-expansion method to the potential KdV and Calogero–Bogoyavlenskii–Schiff equations. We obtain a new solution to these equations like rational function solutions, exponential function, hyperbolic function and trigonometric function. We carry out all the computations in this study with the Wolfram Mathematica 9. In chapter four, we present the two- and three-dimensional graphics of some obtained solutions plotted by using the same program in the Wolfram Mathematica 9. In chapter five, we give a comprehensive conclusion to this study.