Abstract: In this paper the Mathematics-Mechanization method is applied the field of differential equations. A unifying algorithm for constructing solitary wave solutions for a class of nonlinear evolution equations are given, and implemented in a.computer algebraic system.Exact solitary wave solutions of a great deal of nonlinear equations are obtained. The algorithm is based on the fact that the solitary wave solutions are essentially of a localized nature. Seeking solitary wave solutions which are in terms of hyperbolic tangent function gives a nonlinear system of algebraic equations. The system is solved by using Wu Elimination and the exact solutions of nonlinear evolution equation(s) are then obtained.

Key words: Nonlinear evolution equations, Solitary wave solutions, Symbolic computation