On a revisit to the Painlev?? test for integrability and exact solutions for Yang's self-dual equations for e?‘?e?‘? (2) gauge fields

摘要

Painlev?? test (Jimbo et al [1]) for integrability for the Yang's self-dual equations for e?‘?e?‘? (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 Painlev?? 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.