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Zbl 1018.58008
Chan, Hsungrow; Fu, Chun-Chieh; Lin, Chang-Shou
Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation.
(English)
[J] Commun. Math. Phys. 231, No.2, 189-221 (2002). ISSN 0010-3616; ISSN 1432-0916/e

Summary: In this article, we construct self-dual $N$-vortex solutions with a large magnetic flux $\Phi$ of $(2+1)$-dimensional relativistic Chern-Simons model, provided that the coupling constant $\kappa$ is small and the sites of vorticity $\{p_1,\ldots,p_n\}$ satisfies $$\sum_{k\neq j} \log (|p_j-p_k|)\text{ is independent of }j.\tag 1$$ Our solutions exhibit the bubbling phenomenon at each $p_j$. Near each vortex $p_j$, solutions are locally asymptotically symmetric with respect to $p_j$, and the curvature $F_{12}$ tends to a sum of Dirac measures as $\kappa$ tends to zero. By a heuristic argument, it is shown that (1) is also a necessary condition for the existence of multi-vortex solutions which has a locally asymptotically symmetric vortex at $p_j$, $j=1,2,\ldots,N$.
MSC 2000:
*58E50 Appl. of variational methods in infinite-dimensional spaces
81T13 Gauge theories

Keywords: self-dual Chern-Simons-Higgs equation; multi-vortex solutions

Cited in: Zbl 1116.58012

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