$O(4)$-invariant solutions in Yang–Mills theory with scalar field

The representation of 't Hooft is used to establish a correspondence between the class of gauge fields of a non-Abelian Higgs model and the solutions of a scalar field theory with nonlinear interaction. The existence of $O(4)$-invariant instanton type solutions is proved. An explicit example of a nonself-dual instanton is constructed, together with instanton-antiinstanton and meron-instanton pairs.