Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems

We consider the following nonlinear Schrödinger system in R3 {− u + P(|x |)u = μu3 + βv2u, x ∈ R3, − v + Q(|x |)v = νv3 + βu2v, x ∈ R3, where P(r) and Q(r) are positive radial potentials, μ > 0, ν > 0 and β ∈ R is a coupling constant. This type of system arises, in particular, in models in Bose– Einstein condensates theory. We examine the effect of nonlinear coupling on the solution structure. In the repulsive case, we construct an unbounded sequence of non-radial positive vector solutions of segregated type, and in the attractive case we construct an unbounded sequence of non-radial positive vector solutions of synchronized type. Depending upon the system being repulsive or attractive, our results exhibit distinct characteristic features of vector solutions.