Pattern formation via mixed attractive and repulsive interactions for nonlinear Schrodinger systems

Abstract

The paper is concerned with the asymptotic behavior of positive least energy vector solutions to nonlinear Schrodinger systems with mixed couplings which arise from models in Bose-Einstein condensates and nonlinear optics. We show that due to mixed attractive and repulsive interactions the least energy solutions exhibit new interesting component-wise pattern formations, including co-existence of partial synchronization and segregation. The novelty of our approach is the successful use of multiple scaling to carry out a refined asymptotic analysis of convergence to a multiply scaled limiting system. (C) 2016 Elsevier Masson SAS. All rights reserved