Classical, time-independent solutions of the Yang-Mills equations are studied for spherically symmetric situations. In the presence of charge and current distributions the same types of solutions are found as for purely electric sources: Besides the Abelian (Coulomb-Biot-Savart) solution there are two non-Abelian types, one of which requires minimal source strenghts and comes in two branches. The solution pattern is investigated by rough numerical calculations for a simple source model corresponding to spherical shell distributions. In the absence of charge distributions an additional type is found, which has zero electric field and a magnetic field corresponding to a monopole of fixed strength. This type of solution exists for a large class of reasonable source currents. Some analytical examples are given in addition to numerical results for the shell model. Stability problems are not touched.

• Received 13 April 1981

DOI:https://doi.org/10.1103/PhysRevD.25.1123