Abstract
A GL(n,C) self-dual Yang–Mills hierarchy is introduced; it is an infinite system of self-dual Yang–Mills equations having an infinite number of independent variables. Cauchy problems for the hierarchy are formally solved by using Lie transforms of a wave matrix. A relationship between the Kadomtsev–Petviashvili hierarchy and the self-dual Yang–Mills hierarchy is discussed. Furthermore, it is shown that an infinite-dimensional transformation group acts on a solution space to the (n≥2) self-dual Yang–Mills hierarchy. A parametric solution to the hierarchy is also given as a representation of the transformation group.
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