Exact traveling wave solutions to the nonlinear Schrödinger equation

In this paper, through auxiliary equation method we investigate exact traveling wave solutions of the nonlinear Schrödinger equation. As results, we obtain miscellaneous traveling wave solutions including, bright and dark solitons, periodic solutions, singular solutions and exponential solutions. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.