  A fully kinetic simulation approach, treating each plasma component based on
the Vlasov equation, is adopted to study the disintegration of an initial
density perturbation (IDP) into a number of ion-acoustic solitary waves (IASWs)
in the presence of the trapping effect of electrons. The non-linear fluid
theory developed by Schamel has identified three separate regimes of
ion-acoustic solitary waves based on the trapping parameter. Here, the
disintegration process and the resulting self-consistent IASWs are studied in a
wide range of trapping parameters covering all the three regimes continuously.
The dependency of features such as the time of disintegration, the number,
speed and size of IASWs on the trapping parameter are focused upon. It is shown
that an increase in this parameter slows down the propagation of IASWs while
decreases their sizes in the phase space. These features of IASWs tend to
saturate for large value of trapping parameters. The disintegration time shows
a more complicated behavior than what was predicted by the theoretical
approach. Also for the case of trapping parameters bigger than one, propagation
of IASWs is observed in contrast with the theoretical predictions. The kinetic
simulation results unveil a smooth and well-defined dependency of solitary
waves' features on the trapping parameter, showing the possibility of bridging
all the three regimes. Finally, it is shown that for beta around zero, the
electron phase space structure of the accompanying vortex stays symmetric. The
effect of the electron-to-ion temperature ratio on the disintegration and the
propagation of IASWs are considered as a benchmarking test of the simulation
code (in the nonlinear regime).
