Recently I've been looking for massive, 3D symmetrical qballs with various initial heights.
But for initial amplitudes larger than a certain value (which is determined by the other
parameters in the equation of motion of the complex scalar field), I couldn't find their
qball solutions using the usual shooting method. Matt suggested me to test the stability
of the qballs when initial heights are close to the critical value since my fail might
indicate a change in the stability of qballs as initial amplitude increases.

I made two videos; each shows the time evolution of a symmetrical qball (modulus of
the complex scalar field vs. radius) being perturbed by a complex Guassian that has a
fraction of the height of the qball. The first qball has an
initial height significantly smaller than the critical value beyond which no qball could
be found. On the other hand, the initial height of the second qball
is just a bit smaller than the critical value. As shown by the videos, after perturbation,
either of the qballs oscillates at two frequencies simultaneously: the more obvious
up-and-down motion at low freq and the small-amplitude vibration at high freq. In contrast to
to the short qball, tall qball has a smaller amplitude at low-frequency, up-and-down motion
and a larger amplitude at high-frequency vibration. Except for this observation, I haven't
noticed any other significant differences between the qballs' perturbed behaviours.

For fun: a 2-D qball perturbed by a taller Gaussian located
right next to it.

last update: Mon Aug 16, 2010