We present what is to our knowledge the most complete 1-D numerical analysis of the evolution and the propagation
dynamics of an ultrashort laser pulse in a Ti:Sapphire laser oscillator. This study confirms the dispersion
managed model of mode-locking, and emphasizes the role of the Kerr nonlinearity in generating mode-locked
spectra with a smooth and well-behaved spectral phase. A very good agreement with experimental measurements
of pulse energy, spectrum, and temporal width of extracavity compressed pulses is found.