Existence and concentration of ground states of coupled nonlinear Schrödinger equations with bounded potentials

A 2-coupled nonlinear Schrödinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.