Exact traveling wave solutions of some nonlinear evolution equations

Using a traveling wave reduction technique, we have shown that maccari equation, (2+1)-dimensional nonlinear schrödinger 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 schro¨dinger 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 hyperbolic functions, trigonometric functions and rational functions are found out. it is shown that these methods provide a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. a variety of structures of the exact solutions of the elliptic-like equation are illustrated.