The dynamic properties and the analytic solutions of high-order nonlinear time–space fractional Schrödinger equation are studied in this article. Based on a conserved Hamiltonian, the topological structure and the existence of the periodic and soliton solutions are studied by classifying the equilibrium points using thebifurcation method. Moreover, all exact travelling wave solutions are constructed to verify the prior estimation in the qualitative analysis by the complete discrimination system for the polynomial method.