Reduction of the self-dual Yang–Mills equations on subgroups of the extended Poincaré group

We have obtained ansatzes for the vector-potential of the Yang–Mills field in the Minkowski space $R(1,3)$ invariant under 3-parameter subgroups of the extended Poincaré group $\widetilde P(1,3)$. Using these, we carry out symmetry reduction of the self-dual Yang–Mills equations to systems of ordinary differential equations.