Mj. Ablowitz et al., A SELF-DUAL YANG-MILLS HIERARCHY AND ITS REDUCTIONS TO INTEGRABLE SYSTEMS IN 1+1 AND 2+1 DIMENSIONS, Communications in Mathematical Physics, 158(2), 1993, pp. 289-314
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'' in
tegrable hierarchy. Prototypical examples of reductions to classical s
oliton equations are presented and related issues such as recursion op
erators, symmetries, and conservation laws are discussed.