Instanton chains with multimonopole limits: Lax pairs for non-axially-symmetric cases

Abstract

A formalism is proposed for constructing sequences of instantons which give, in a simple scaling limit, separable multimonopole solutions. For this purpose essentially static techniques are adapted to the construction of finite-action solutions through a trick already used before for the axially symmetric case. For going beyond axial symmetry appropriate Lax pairs are constructed. Then, in the framework of Zakharov et al. for purely solitonic solutions, pole equations are solved and a suitable seed solution ${\psi }_{\mathrm{}\left(0\right)\mathrm{}}$ obtained. The restriction to axial symmetry in this framework is presented. The corresponding results in the monopole limit are shown to emerge trivially from those for instantons.