On coupled nonlinear Schrodinger equations with harmonic potential

The initial value problem for some coupled nonlinear Schrodinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. For the focusing sign, existence of global and non global solutions is discussed via potential well method. Moreover, existence of ground state and instability of standing waves are proved.
Comment: arXiv admin note: text overlap with arXiv:1505.07506, arXiv:1505.07059, arXiv:1505.08101, arXiv:1505.08096