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

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