  Some well known gauge scalar potential very often considered or used in the
literature are investigated by means of the classical Yang Mills equations for
the $SU(2)$ subgroups of $N_c=3$. By fixing a particular shape for the scalar
potential, the resulting vector potentials and the corresponding color-charges
sources are found. By adopting the spherical coordinate system, it is shown
that spherically symmetric solutions, only dependent on the radial coordinate,
are only possible for the Abelian limit, otherwise, there must have
angle-dependent component(s). The following solutions for the scalar potential
are investigated: the Coulomb potential and a non-spherically symmetric
generalization, a linear potential $A_0 (\vec{r}) \sim (\kappa r)$, a
Yukawa-type potential $A_0 (\vec{r}) \sim (C e^{-r/r_0}/r)$ and finite spatial
regions in which the scalar potential assumes constant values. The
corresponding chromo-electric and chromo-magnetic fields, as well as the
color-charge densities, are found to have strong deviations from the spherical
symmetric configurations. We speculate these types of non-spherically symmetric
configurations may contribute (or favor) for the (anisotropic) confinement
mechanism since they should favor color charge-anti-charge (or
three-color-charge) bound states that are intrinsically non spherically
symmetric with (asymmetric) confinement of fluxes. Specific conditions and
relations between the parameters of the solutions are also presented.
