  An exact solution for an SU(2) Yang-Mills field coupled to a scalar field is
given. This solution has potentials with a linear and Coulomb part. This may
have some physical importance since many phenomenological QCD studies assume a
linear plus Coulomb potential. Usually the linear potential is motivated with
lattice gauge theory arguments. Here the linear potential is an exact result of
the field equations. We also show that in the Nielsen-Olesen Abelian model
there is an exact solution in the BPS limit which has a Coulomb-like
electromagnetic field and a logarithmically rising scalar field. Both of these
solutions must be cut off from above to avoid infinite field energy.
