Abstract
In this paper, with the aid of computer symbolic computation system such as Maple, an algebraic method is firstly applied to two nonlinear evolution equations, namely, nonlinear Schrodinger equation and Pochhammer-Chree (PC) equation. As a consequence, some new types of exact traveling wave solutions are obtained, which include bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.