The object of this work is to obtain the similarity solution of a given problem by applying the Group and Potential similarity transformation methods where the governing partial differential equations are written in a conserved form to obtain new simpler system of partial differential equations. We then applied the group method which reduces the new system with the auxiliary condition to a system of ordinary differential equation with the appropriate corresponding conditions that can be solved analytically or numerically. Because of the absence of this combination between the potential and the group methods so far, this search is considered as an innovation in the field of mathematics
