Painlevé test for integrability for a combination of Yang’s self-dual equations for SU (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics and a comparative discussion among the three

Painlevé test for integrability for the combined equations generated from Yang’s self-dual equations for SU (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics faces some peculiar situations that allow none of the stages (leading order analysis, resonance calculation and checking of the existence of the requisite number of arbitrary functions) to be conclusive. It is also revealed from a comparative study with the previous results that the existence of abnormal behaviour at any of the stated stages may have a correlation with the existence of chaotic property or some other properties that do not correspond to solitonic behaviour.