General solutions of Witten's gauge-field equations (Q1057561)

This paper is concerned with 8-dimensional generalisations of the self- dual Yang-Mills equations, introduced by \textit{E. Witten} [Phys. Lett. B 77, 394-398 (1978)]. They are shown to be special cases of another system noted by \textit{R. Ward} [Nucl. Phys. B 236, 381-396 (1984)]. Formal power series solutions depending on initial data involving arbitrary holomorphic functions are described, and the relationship of the two systems discussed. It seems likely that the twistor theory of \({\mathbb{R}}^ 8\) considered as an Sp(2) manifold is an equivalent way of formulating some of these results, following the lines developed by \textit{S. Salomon} [''Quaternionic structures and twistor spaces'' in Global Riemannian geometry, Eds. T. J. Willmore and N. J. Hitchin, Ellis Horwood Ltd., Chichester (1984)].