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

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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.
Publisher
SPRINGER BASEL AG
Issue Date
2017-03
Language
English
Article Type
Article
Keywords

LEAST-ENERGY SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC-SYSTEMS; STANDING WAVES; R-N; STATES; EXISTENCE; MULTIPLE; COMPETITION; SYMMETRY

Citation

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, v.19, no.1, pp.559 - 583

ISSN
1661-7738
DOI
10.1007/s11784-016-0365-1
URI
http://hdl.handle.net/10203/223473
Appears in Collection
MA-Journal Papers(저널논문)
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