Uniqueness of minimal blow-up solutions to nonlinear Schrödinger system

In this paper, we are concerned with the finite time blow-up solutions to the following N coupled nonlinear Schrödinger system in R2: (0.1)i∂tϕj+Δϕj+∑k=1Najk|ϕk|2ϕj=0, where N≥2 and the coefficient matrix A satisfies ajk=akj>0. We study the properties of the blow-up solutions which obtain the minimal L2-norm, and prove that such solution is unique, up to the symmetries of the system.