Algebro-geometric constructions of the Wadati-Konno-Ichikawa flows and applications

With the aid of Lenard recursion equations, we derive the Wadati-Konno-Ichikawa hierarchy. Based on the Lax matrix, an algebraic curve of arithmetic genus n is introduced, from which Dubrovin-type equations and meromorphic function phi are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of phi and the algebro-geometric characters of . Copyright (c) 2015John Wiley & Sons, Ltd.