Abstract
In this paper, we apply the auxiliary equation method with the aid of symbolic computer algebra system (CAS) such as Maple or Mathematica to construct many new exact traveling wave solutions of a singularly perturbed generalized Gardner equation with nonlinear terms of any order. Using a simple transformation, this equation can be reduced to a nonlinear ordinary differential equation (ODE). A comparison between our results and the well-known results is given. Further, plotting 2D and 3D graphics of the exact solutions are shown.