We study the following nonlinear Schrödinger system. {-δu+P(|x|)u=μu3+βv2u, x∈R2,-δv+Q(|x|)v=vu3+βu2v, x∈R2,where P(r) and Q(r) are positive radial functions. μ>0,v>0, and β∈R is a coupling constant. This type of system arises, particularly, in models in Bose-Einstein condensates theory. Applying a finite reduction method, we construct an unbounded sequence of non-radial positive vector solutions of segregated type when β is in some suitable interval, which gives an answer to an interesting problem raised by Peng and Wang in Remark ...
