eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2020-08-22 8 4 70 74 10.12691/tjant-8-4-1 TJANT2020841 article Guoqiang Dang dangguoqiang@126.com 1 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, China We show abundant simply periodic solutions, trigonometric solutions, hyperbolic function solutions and Weierstrass elliptic solutions of the reduction of the cubic nonlinear Schrödinger equation by the complex method with Painlevé analysis, and some solutions appear to be new. At last, we give some computer simulations to illustrate our main results. http://pubs.sciepub.com/tjant/8/4/1/tjant-8-4-1.pdf Schr?dinger equations exact solutions Weierstrass elliptic function solutions complex method