Considering the many models of nonlinear partial differential equations existing in physics and other fields， the existence of exact travelling wave solutions of equations was proposed． By introducing a wave variable and using the first integral method based on the ring theory of commutative algebra，we have obtained the exact travelling solitary wave solutions for two nonlinear evolution equations.It has many advantages over other traditional techniques, it is direct and concise.It also shows that the first integral method is an effective method with great potentials when finding complex solitary wave solutions of the nonlinear equations．