Abstract
The Yang–Mills equations for gauge fields of an arbitrary semisimple Lie group G in Euclidean spaces Rn with dimension n≥4 is considered. For gauge fields Aa we introduce the ansätze which reduce the Yang–Mills equations in Rn to a set of nonlinear differential matrix equations (Rouhani–Ward equations). This permits us to write out the explicit form of cosmological, plane-wave, and other types of solutions.
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