  The paper, classically, presents an extended Klein-Gordon field system in 3+1
dimensions with a special Q-ball solution. The Q-ball solution is energetically
stable, that is, for any arbitrary small deformation above the background of
that, total energy always increases. The general dynamical equations, just for
this special Q-ball solution, are reduced to the known versions of a complex
nonlinear Klein-Gordon system, as its dominant dynamical equations.
