Based on the Green function method, the nonlinear Schrödinger equation is directly solved in the time domain (without Fourier transform). Because the dispersion and nonlinear effects are calculated simultaneously, it does not bring any spurious effect such as the split-step method in which the step size has to be carefully controlled by an error estimation. By this time domain solution, the pulse fission is analyzed, and we obtain the relationship between the minimum T₀ (the half-width at 1/e-intensity point of a pulse) and dispersion coefficients (β₂, β₃, and β₄). Thus the concrete dispersion values, which have an impact on ultrashort pulses (the quantity units is femtosecond or attosecond), are listed. It has been demonstrated that pulse fission occurs in the normal and anomalous dispersion regimes, even though fourth-order dispersion and the fifth-order nonlinear effects are not taken into account.