Nontopological first-order vortices in a gauged $CP(2)$ theory endowed with the Chern-Simons action

We study a gauged $CP(2)$ scenario model with the Chern-Simons term, focusing our attention on those time-independent radially symmetric configurations with nontopological profile. We proceed the minimization of the effective energy in order to introduce the corresponding first-order framework, from which we define a legitimate self-dual scenario. We solve the resulting first-order equations numerically by means of the finite-difference scheme, from which we depict the nontopological solutions. We also identify a special kind of solutions which can be partially described by an analytical treatment.