My research interest mainly is focused on solving for exact wave solutions of nonlinear evolution equations, specifically related to the Burgers' equation, such as perturbed Burgers equation. This type of equation occurs in many physical systems. Their solutions may describe various phenomena in physics and other fields. Various methods such as the inverse scattering method, Hirota method, the hyperbolic tangent method; the analytic method; the method of determined coefficients; and Painleve analysis will be the main tools for the investigation. By examining all these methods we try to find a possible way of solving the related Burgers' equation, hopefully obtaining an exact solution.