Groups of equivariant loops in SL(n+1,C) and soliton equations

Abstract

This article studies a generalization of the Drinfel’d and Sokolov hierarchies for sln+1 and shows how the dressing transformation [as interpreted by Segal and Wilson, Publ. Math. IHES 61, 5 (1985)] produces a large class of almost globally analytic solutions. Many of these solutions are ‘‘of finite type,’’ i.e., related to the Jacobian of a complete algebraic curve.