Dynamic properties of the cubic nonlinear Schrödinger equation by symplectic method

The dynamic properties of a cubic nonlinear Schr?dinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schr?dinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.