Pattern formation via mixed attractive and repulsive interactions for nonlinear Schrödinger systems. (English. French summary) Zbl 1345.35032
Authors’ abstract: The paper is concerned with the asymptotic behavior of positive least energy vector solutions to nonlinear Schrödinger 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 an 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.
Reviewer: Junichi Aramaki (Saitama)
MSC:
| 35J50 | Variational methods for elliptic systems |
| 35J57 | Boundary value problems for second-order elliptic systems |
| 35J60 | Nonlinear elliptic equations |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
mixed interactions; nonlinear Schrödinger systems; multiple scaling; partial synchronization and segregationReferences:
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