  Nonlinear solitary solutions to the Vlasov-Poisson set of equations are
studied in order to investigate their stability by employing a fully-kinetic
simulation approach. The study is carried out in the ion-acoustic regime for a
collisionless, electrostatic and Maxwellian electron-ion plasma. The trapped
population of electrons is modeled based on well-known Schamel distribution
function. Head-on mutual collisions of nonlinear solutions are performed in
order to examine their collisional stability. The findings include three major
aspects: (I) These nonlinear solutions are found to be divided into three
categories based on their Mach numbers, i.e. stable, semi-stable and unstable.
Semi-stable solutions indicates a smooth transition from stable to unstable
solutions for increasing Mach number. (II) The stability of solutions is traced
back to a condition imposed on averaged velocities, i.e. net neutrality. It is
shown that a bipolar structure is produced in the flux of electrons,early in
the temporal evolution. This bipolar structure acts as the seed of the
net-neutrality instability, which tips off the energy balance of nonlinear
solution during collisions. As the Mach number increases, the amplitude of
bipolar structure grows and results in a stronger instability. (III) It is
established that during mutual collisions, a merging process of electron holes
can happen to a variety of degrees, based on their velocity characteristics.
Specifically, the number of rotations of electron holes around each other (in
the merging phase) varies. Furthermore, it is observed that in case of a
non-integer number of rotations, two electron holes exchange their phase space
cores.
