Painlev{\'e} singularity structure analysis of three component Gross-Pitaevskii type equations

In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlev\'e singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlev\'e test.