A SELF-DUAL YANG-MILLS HIERARCHY AND ITS REDUCTIONS TO INTEGRABLE SYSTEMS IN 1+1 AND 2+1 DIMENSIONS

The self-dual Yang-Mills equations play a central role in the study of integrable systems. In this paper we develop a formalism for deriving a four dimensional integrable hierarchy of commuting nonlinear flows containing the self-dual Yang-Mills flow as the first member. We show that upon appropriate reduction and suitable choice of gauge group it produces virtually all well known hierarchies of soliton equations in 1 + 1 and 2 + 1 dimensions and can be considered as a ''universal'' integrable hierarchy. Prototypical examples of reductions to classical soliton equations are presented and related issues such as recursion operators, symmetries, and conservation laws are discussed.