Dynamic properties of cubic nonlinear Schrödinger equation with varying nonlinear parameter

The dynamic properties of the cubic nonlinear Schrodinger equation are investigated numerically using the symplectic scheme (Euler centred scheme). We discuss the dynamic behaviour of the cubic nonlinear Schrodinger equation with varying nonlinear parameter. The results show that the system exhibits regular recurrence for weakly nonlinearity. We also illustrate that the system will exhibit varying dynamic behaviour with increasing nonlinear parameter, i.e. the system will show the homoclinic orbit (HMO) crossing, quasi-recurrence, pseudorecurrence, irregular motion or stochastic motion for a strongly nonlinear constants.