Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation
Journal
Communications in Mathematical Physics
Journal Volume
231
Journal Issue
2
Pages
189-221
Date Issued
2002
Author(s)
Abstract
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 x is small and the cites of vorticity {p1, . . ., pn} satisfies ∑log(|pj - pk|) is independent of j. Our solutions exhibit the bubbling phenomenon at each pj. Near each vortex pj, solutions are locally asymptotically symmetric with respect to pj, and the curvature F12 tends to a sum of Dirac measures as k tends to zero. By a heuristic argument, it is shown that (0.1) is also a necessary condition for the existence of multi-vortex solutions which has a locally asymptotically symmetric vortex at pj, j = 1, 2, . . ., N.
Type
journal article