On a revisit to the Painleve test for integrability and exact solutions for Yang's self-dual equations for SU(2) gauge fields

Painleve test for integrability for the Yang's self-dual equations for SU(2) gauge fields has been revisited. Jimbo et. al. analysed the complex form of the equations with a rather restricted form of singularity manifold. They did not discuss exact solutions in that context. Here the analysis has been done starting from the real form of the same equations and keeping the singularity manifold completely general in nature. It has been found that the equations, in real form, pass the Painleve test for integrability. The truncation procedure of the same analysis leads to non-trivial exact solutions obtained previously and auto-Backlund transformation between two pairs of those solutions. (author)