Partly clustering solutions of nonlinear Schrodinger systems with mixed interactions

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In this paper, we prove a partly clustering phenomenon for nonlinear Schrodinger systems with large mixed couplings of attractive and repulsive forces, which arise from the models in Bose-Einstein condensates and nonlinear optics. More precisely, we consider a system with three components where the interaction between the first two components and the third component is repulsive, and the interaction between the first two components is attractive. Recent studies [10-13] in this case show that for large interaction forces, the first two components are localized in a region with a small energy and the third component is close to a solution of a single equation. Especially, the results in the works [12,13] say that the region of localization for a (locally) least energy vector solution on a ball in the class of radially symmetric functions is the origin or the whole boundary depending on the space dimension 1 <= n <= 3. In this paper we construct a new type of solutions with a region of localization different from the origin or the whole boundary. In fact, we show that there exist radially symmetric positive vector solutions with clustering multi-bumps for the first two components near the maximum point of r(n-1)U(3), where U is the limit of the third component and the maximum point is the only critical point different from the origin and the boundary. (C) 2021 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2021-06
Language
English
Article Type
Article
Citation

JOURNAL OF FUNCTIONAL ANALYSIS, v.280, no.12

ISSN
0022-1236
DOI
10.1016/j.jfa.2021.108987
URI
http://hdl.handle.net/10203/282786
Appears in Collection
MA-Journal Papers(저널논문)
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