Abstract: In this paper, we use an effective method which is the rational sine-Gordon expansion method to present new wave simulations of a governing model. We consider the (1+1)-dimensional conformable Fisher equation which is used to describe the interactive relation between diffusion and reaction. Various types of solutions such as multi-soliton, kink, and anti-kink wave soliton solutions are obtained. Finally, the physical behaviours of the obtained solutions are shown by 3D, 2D, and contour surfaces.