Behzad Ghanbari

Nonlinear partial differential equations (NPDE) is an inevitable mathematical tool tool to explore a large variety of engineering and physical phenomena. Duo to this importance, many mathematical approaches have been established to seek their travelling wave solutions. In this paper, we have examined the Gardner equation via two well-known analytical approached, namely the improved tan(Θ(#))-expansion method and the wave ansatz method. The solutions comprise bright, dark, singular and W-shaped soliton solution. One can see that methods are relatively easy and efficient to use. To better understand the characteristics of the theoretical results several numerical simulations are carried out.