Victor Enolski (Institute of Magnetism NASU, Kyiv, Ukraine)

Theta-functional solutions to the Bogomolny equation

We are developing the Nahm construction to solve Bogomolby equation for monopole of higher charges. By following Nahm we reduce the the Weyl equation written for 2n spinors to to matrix n-dimensional spectral on the interval [0,2] problem and solve the last one by method of Baker-Akhiezer function. The Higgs field and gauges are then expressed in terms of residues of the Baker-Akhiezer function at the boundaries of the interval.