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Lee, Youngae
Nonlinear Analysis Lab.
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Bubbling solutions of mixed type for a general non-Abelian Chern-Simons-Higgs system of rank 2 over a torus

Author(s)
Huang, Hsin-YuanLee, YoungaeMoon, Sang-Hyuck
Issued Date
2022-01
DOI
10.1016/j.na.2021.112552
URI
https://scholarworks.unist.ac.kr/handle/201301/55111
Fulltext
https://www.sciencedirect.com/science/article/pii/S0362546X21001905?via%3Dihub
Citation
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v.214, pp.112552
Abstract
We consider a general non-Abelian Chern-Simons-Higgs system of rank 2 Delta u(i) + 1/epsilon(2) (Sigma(2)(j=1) K(ji)e(uj) - Sigma(2)(j=1)Sigma(2)(k=1) K(kj)K(ji)e(uj) e(uk)) = 4 pi Sigma(N)(l=1) m(i,l)delta(pl) (i = 1, 2) (0.1) over a flat torus, where m(1,) (l) >= 0, m(2, l) >= 0, ( m(1,l), m(2, l)) not equal (0, 0) for l = 1,..., N, delta(p) is the Dirac measure at p, K is a non-degenerate 2 x 2 matrix of the form K = (1 + a -a -b 1 + b). When a > -1, b > -1, and a + b > -1, Eqs (0.1) are expected to have three types solutions: topological, non-topological and mixed type solutions. Concerning the existence of various type solutions, there are requirements that a > 0 and b > 0, or a and b are close to 0 in the literature. It is still open for generic a and b. We partially answer this question and show that (0.1) possesses bubbling mixed type solutions provided that epsilon is small and (a, b) satisfies (1.17). (C) 2021 Elsevier Ltd. All rights reserved.
Publisher
Pergamon Press Ltd.
ISSN
0362-546X
Keyword (Author)
Non-Abelian Chern-Simons modelsBubbling mixed type solutions
Keyword
EXISTENCEVORTICESMODELEQUATION

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