  In the first part of this paper, the different distinguishable pathways and
regions of the single and sequential double ionization are determined and
discussed. It is shown that there are two distinguishable pathways for the
single ionization and four distinct pathways for the sequential double
ionization. It is also shown that there are two and three different regions of
space which are related to the single and double ionization respectively. In
the second part of the paper, the time dependent Schr\"{o}dinger and Newton
equations are solved simultaneously for the electrons and the nuclei of H$_2$
respectively. The electrons and nuclei dynamics are separated on the base of
the adiabatic approximation. The soft-core potential is used to model the
electrostatic interaction between the electrons and the nuclei. A variety of
wavelengths (390 nm, 532 nm and 780 nm) and intensities ($5\times10^{14}$
$Wcm^{-2} $ and $ 5\times10^{15}$ $Wcm^{-2}$) of the ultrashort intense laser
pulses with a sinus second order envelope function are used. The behaviour of
the time dependent classical nuclear dynamics in the absence and present of the
laser field are investigated and compared. In the absence of the laser field,
there are three distinct sections for the nuclear dynamics on the electronic
ground state energy curve. The bond hardening phenomenon does not appear in
this classical nuclear dynamics simulation.
