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Reduction of self-dual Yang – Mills equations with respect to subgroups of the extended Poincaré group

Classical SU(2)-invariant Yang–Mills equations (YME) comprise a system of twelve nonlinear partial differential equations (PDE) of the second order in the Minkowski space R(1, 3). On the other hand, once the Yang–Mills potentials satisfy the selfduality conditions, the YME are automatically satisfied. This allows one to construct a broad subclass of solutions to the YME using the condition of self-duality, which amounts to a system of nine first-order PDE,