Some New Exact Traveling Wave Solutions for the Zhiber-Shabat Equation

In this paper, we implemented a very important method to solve nonlinear partial differential equations known as the exp(-Φ(ξ))-expansion method. Recently, there are several methods being constructed for finding analytical solutions of nonlinear partial differential equations. However, the exp(-Φ(ξ))-expansion method is more effective and useful for solving the nonlinear evolution equations. With the help of this method, we are investigated the exact traveling wave solutions of the Zhiber-Shabat equation. The obtaining exact solutions of this equation are describe many physical phenomena in mathematical physics such as solid state physics, plasma physics, nonlinear optics, chemical kinetics and quantum field theory. Further, three-dimensional plots of the solutions such as solitons, cuspon, periodic, singular kink and bell type are also given to visualize the dynamics of the equation.