Multi-peak solutions for nonlinear Schrödinger systems with magnetic potentials in R3R3

We study the following nonlinear Schrödinger system with magnetic potentials in R3R3{(ϵ∇i−A(x))2u+P(x)u=μ1|u|2u+β|v|2u,x∈R3,(ϵ∇i−A(x))2v+Q(x)v=μ2|v|2v+β|u|2v,x∈R3, where ϵ>0ϵ>0 is a small parameter, μ1,μ2>0μ1,μ2>0 and β>0β>0 is a coupling constant. A(x)A(x), P(x)P(x) and Q(x)Q(x) are potential functions. Applying the finite reduction method, we prove that the nonlinear Schrödinger system has multi-peak solutions under some suitable conditions which are given in Section 1.