Nonlinear Schrodinger systems with trapping potentials for mixed attractive and repulsive interactions

Abstract

In this paper, we prove the existence of a positive least energy vector solution and its asymptotic behavior for three-component nonlinear Schrodinger systems with mixed couplings (two repulsive and one attractive) forces and nonconstant potentials on the entire space when the interaction forces are large. When the system with mixed coupling forces has constant potentials, repulsive forces make a state more stable when the interaction between components are less; thus it loses a compactness due to translation segregating components. To get a compactness, we impose a potential wall at infinity; then, we can construct a least energy vector solution. A main interest in this work is its asymptotic behavior of the solution for large interaction forces; one component repelling other two components survives and the other two components diminish and concentrate at a point diverging to infinity as the interaction forces are getting larger and larger. The location of the concetration point, which we could characterize in terms of the limit of a surviving component, a repulsive force and potentials of diminishing components under the assumption of the nondegeneracy for the limit problem of the surviving component.