On the blowup phenomenon for N-coupled focusing Schrödinger system in .d (d . 3)

We study blow-up, global existence and ground state solutions for the N-coupled focusing nonlinear Schrödinger equations. Firstly, using the Nehari manifold approach and some variational techniques, the existence of ground state solutions to the equations (CNLS) is established. Secondly, under certain conditions, finite time blow-up phenomena of the solutions is derived. Finally, by introducing a refined version of compactness lemma, the L 2 concentration for the blow-up solutions is obtained.