Concentrating solutions of nonlinear Schrödinger systems with mixed interactions

In this paper we study the existence of solutions to nonlinear Schrödinger systems with mixed couplings of attractive and repulsive forces, which arise from the models in Bose-Einstein condensates and nonlinear optics. In particular, we build solutions whose first component has one bump and the other components have several peaks forming a regular polygon around the single bump of the first component.