In this paper, we investigate the (2+1)-dimensional Broer-Kaup-Kupershmidt equation employing the truncated Painleve approach and we generate localized solutions like dromions, lumps, and rogue waves. The collisional dynamics of the localized solutions is then studied. While the dromions are found to undergo inelastic collision exchanging energy among them, the lumps are found to be noninteracting. We also bring out the unstable nature of rogue waves.