Riemann-Hilbert Transforms and Bianchi-Bäcklund Transformations for the Supersymmetric Yang-Mills Fields

Riemann-Hilbert transforms, and their connections with the affine Lie algebra of Kac and Moody, and a two-parameter Bianchi-Bäcklund transformation are given for the constraint equations for the supersymmetric Yang-Mills fields. These are important integrable properties of the supersymmetric Yang-Mills fields; especially for $N>~3$ these constraint equations give equations of motion of the fields.