Integral equations for extended solutions in field theory: Monopoles and dyons

Abstract

In this paper we give a simple method to obtain extended solutions of nonlinear classical field theories. The technique applies to problems where the boundary values at either end of the domain are specified, and consists of converting the set of field equations to a system of coupled nonlinear integral equations that can be solved numerically by simple iteration. As an illustration, the 't Hooft monopole and the Julia-Zee dually charged monopole system are studied in detail. The physical structure of these extended solutions and the possible effects of quantum fluctuations are briefly discussed.