  Nonlinearities imbedded in the Lagrange density for non-Abelian gauge
theories produce solutions to the Yang-Mills Maxwell equations that describe
spatially extended chromostatic condensates. For solutions in
spherically-symmetric SU(2) the topological structures separating such
condensates provide a specific solitonic description of color confinement. The
strong Conjecture The confinement mechanism for QCD involves a domain wall of
topological (CP-odd) charge separating the interior volume of hadrons from an
exterior volume. To explain the consequences of this conjecture we describe
spherically symmetric chromostatic condensates that are consistent with the
interior volume of a hadron and other condensates that are consistent with
exterior vacuum volume. We then demonstrate how the Yang-Mills Maxwell
equations can connect the two volumes with a soliton domain wall. The
preliminary phenomenological description described here does not deal
explicitly either with charged fermions or with the quantization of non-Abelian
dynamics.
