Exact Solutions of a Cubic Nonlinear Schrödinger Equation with Dispersion and Nonlinear Effect Terms

In this ariticle, a cubic nonlinear Schrödinger equation with third-order dispersion and nonlinear effect terms(self-steepening and self-frequency shift terms) is considered. The solutions of the cubic nonlinear Schrödinger equation are obtained by using the complete discrimination system for polynomial method. These solutions include solitary wave solutions, rational function solutions and Jacobian elliptic function periodic solutions, which describe the propagation characteristics of waves in corresponding applications. Finally, the relevant graphs of the obtained solutions are drawn.