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Bäcklund transformations for the anti-self-dual Yang-Mills equations. (English) Zbl 0649.58042

Summary: Beginning from any given (local) solution of the GL(n,\({\mathbb{C}})\) anti- self-dual Yang-Mills 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.

MSC:

58Z05 Applications of global analysis to the sciences
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
81T08 Constructive quantum field theory
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