Abstract
In this paper, by using the transformation introduced in Acta Phys. Sin., 53 (2004) 2828, a nonlinear partial differential equation can be reduced to a nonlinear ordinary differential equation, and then solve it by the ansatz technique and with the aid of Mathematica. As a result, abundant types of explicit and exact solutions to the KdV equation and the KdV-Burgers equation, which include the solitary wave solutions, the singular traveling wave solutions, the trigonometric function periodic wave solutions, are successfully obtained.
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