Pattern formation via mixed interactions for coupled Schrödinger equations under Neumann boundary condition

Abstract

This paper is a sequel to Byeon et al. (J Math Pures Appl 106(9):477–511, 2016) concerning the asymptotic behavior of positive least energy vector solutions to nonlinear Schrodinger systems with mixed couplings that arise from models in Bose–Einstein condensates and nonlinear optics. In [8] we treated homogeneous Dirichlet boundary condition. In the current paper we investigate the case of homogeneous Neumann boundary condition. We show that due to mixed attractive and repulsive interactions the least energy solutions exhibit component-wise pattern formations, in particular, co-existence of partial synchronization and segregation. We employ multiple scalings to carry out a refined asymptotic analysis of convergence to a multiple scaled limiting system.