Bäcklund transformations for the anti-self-dual Yang–Mills equations

Abstract

Beginning from any given (local) solution of the GL(n,C) anti-self-dual Yang–Mills (ASDYM) equations on Minkowski space, a simple technique for the generation of large classes of solutions (perhaps in some sense all) is given. The origin of this technique is described in terms of two versions of the Ward construction. The resulting description of Bäcklund transformations is sufficiently simple that it is then possible to identify the group generated by the collection of all such Bäcklund transformations and the space on which it acts in terms of concrete functions.