Abstract: The dynamic properties of nonlinear Schrödinger equations are investigated numerically by using the symplectic scheme (Euler centered scheme). The dynamic behavior of cubic nonlinear Schrödinger equations with various nonlinear parameter is studied in different phase space.And the dynamic properties of cubic-quintic nonlinear Schrödinger equations are dealt with numerically by using the symplectic scheme. The dynamic behaviors of cubic-quintic nonlinear Schrödinger equations with different cubic and quintic nonlinear parameters are discussed in the phase space.It shows that the route varies with different cubic nonlinear parameters and with the increase of the quintic nonlinear parameters.

Key words: nonlinear Schrödinger equation, phase space, symplectic algorithm