Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation

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 κ is small and the cites of vorticity satisfies

.

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 (0.1) is also a necessary condition for the existence of multi-vortex solutions which has a locally asymptotically symmetric vortex at .