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Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation. (English) Zbl 1018.58008

Summary: In this article, we construct self-dual N-vortex solutions with a large magnetic flux Φ of (2+1)-dimensional relativistic Chern-Simons model, provided that the coupling constant κ is small and the sites of vorticity {p 1 ,...,p n } satisfies

kj log(|p j -p k |)isindependentofj·(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 κ 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,...,N.

58E50Applications of variational methods in infinite-dimensional spaces
81T13Yang-Mills and other gauge theories