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We study the nonlinear parabolic Fisher’s equations for travelling wave solutions. The analyses focus on to describe the analytic solution in the spatial pattern of travelling wave solutions; especially the solutions are characterized in invariant with respect to translation in space. There are two phases in the work: in the first stage, we analyze dimensional reaction-diffusion equation with logistic type growth while in the second phase the non-dimensional equation known as Fishers’ equation is studied numerically. To investigate the results numerically, we select the explicit-implicit finite difference method (FDM) and the approximate solutions are compared with the exact solution in different time steps.