Lesser known Nahm approach in algebro-geometric description of monopole fields

Abstract: In the ADHMN-construction (Atiyah-Drinfeld-Hitchin-Manin-Nahm) calculation of the monopole fields- Higgs field and gauges - reduced to solving linear ODE - Weyl equations with "potentials'" are given by the so called Nahm data. Even in the case of charge two, when the Nahm data represent elliptic functions, the analytic expressions for the monopole fields are unknown until now. We overcome the problem using a lesser known Nahm approach (compared to the ADHMN construction), whose implementation leads to a complete description of monopole fields in terms of algebraic functions and incomplete elliptic integrals.