On the solutions of SU(2)/U(1) harmonic equations in the gauge theories

Within the harmonic approach a self-duality equation, solutions of superfield constraints in the supergauge theory SYM42, and other nonlinear problems in gauge theories may be reduced to universal linear differential equations for the 'bridge' matrix h or harmonic connection A(-2). We consider a wide class of explicit solutions for h and A(-2), which can be obtained by quadratures using a special harmonic parametrization of the analytical prepotential. This method gives a general solution in the case of SYM42. (orig.)