The analytic solutions of Schr?dinger equation with Cubic-Quintic nonlinearities

摘要

This paper deals with the nonlinear Schr?dinger equation with Cubic-Quintic nonlinearities. After transforming the non-autonomous nonlinear Schr?dinger equation into a stationary equation by adopting the BPVK idea, we give the classification of the solutions to the Cubic-Quintic nonlinear Schr?dinger equation by utilizing the complete discrimination system for polynomial method. As an auxiliary result, we use the homotopy renormalization method (HTR) to obtain the global solutions to the Ermakov-Pinney equation satisfied by the width function.