First integrals and Yoshida analysis of Nahm's equations

Abstract

First integrals of Nahm's equations for monopole solutions in Yang-Mills theories are explicitly given for various special cases. Taking into account the scale invariance, all Kowalewski exponents are determined. Both the polynomial first integrals and the Kowalewski exponents are obtained with the help of a REDUCE program package. This leads to a completely consistent picture in the sense of the analysis recently proposed by Yoshida (1983).