Self-duality equation: monodromy matrices and algebraic curves

It is shown that the general local solution of the self-duality equation with $SU(1,1)$ and $SU(2)$ gauge groups is associated to some algebraic curve with moving branch points if related “monodromy matrix” is rational. The “multisoliton” solutions including monopoles and instantons correspond to the degenerated curves, when the branch cuts collapse to the double points. Bibliography: 17 titles.