THE τ FUNCTIONS OF THE AKS HIERARCHY AND TWISTOR CORRESPONDENCE

Abstract

Adler–Kostant–Symes scheme provides a geometrical method for constructing different integrable systems. We construct an AKS hierarchy and obtain the τ function solutions of this hierarchy. We also show that this AKS hierarchy is a reduction of self dual Yang–Mills (SDYM) equation hierarchy and discuss its twistor construction. Hence we re-establish once again that SDYM hierarchy is a universal integrable hierarchy, so that by appropriate reduction and suitable choice of gauge group this hierarchy produces all the well-known hierarchies of the soliton equations 1.