New Generalized (G′/G)-expansion Method to the Zhiber-Shabat Equation and Liouville Equations

This paper presents the implementation of the new extended -expansion method to the Zhiber-Shabat equation and the Liouville equation. Using this method, a variety of explicit travelling wave solutions has been generated. Results also show that the obtained solutions are exclusively new and, the implemented scheme has significant improvement against other methods. Finally, the work presents here the profound implications for future studies of nonlinear evolution equations in visualizing the dynamics of the equations and may help to describe physical phenomena in mathematical physics.