Solutions of Yang–Mills and Yang–Mills–Higgs equations

The Yang–Mills (YM) and Yang–Mills–Higgs (YMH) models are considered for arbitrary semisimple gauge Lie groups $G$. Ansatzes are introduced that reduce the YM and YMH equations to the equations of the model of a scalar field and ordinary differential equations (Nahm equations). With each solution of these equations there is associated a solution of the YM equations of instanton type or a solution of the YMH equations of monopole type. Solutions for the groups SU(2) and SU(3) are given as examples.