Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrodinger equation, medium equal width equation, (3?1)-dimensional modified KdV-Zakharov- Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrodinger equation can be reduced to the same family of auxiliary elliptic-like equations. Then using extended F-expansion and projective Riccati equation methods, many types of exact traveling wave solutions are obtained. With the aid of solutions of the elliptic-like equation, more explicit traveling wave solutions expressed by the hyper- bolic functions, trigonometric functions and rational func- tions are found out. It is shown that these methods provide a powerful mathematical tool for solving nonlinear evolu- tion equations in mathematical physics. A variety of structures of the exact solutions of the elliptic-like equation are illustrated.