Bubbling Solutions for the SU(3) Chern-Simons Model on a Torus



We consider the following nonlinear system derived from the SU(3) Chern-Simons models on a torus Ω:

equation image

where equation image denotes the Dirac measure at equation image. When equation image, if we look for a solution with equation image, then (0.1) is reduced to the Chern-Simons-Higgs equation:

equation image

The existence of bubbling solutions to (0.1) has been a longstanding problem. In this paper, we prove the existence of such solutions such that equation image even if equation image. © 2012 Wiley Periodicals, Inc.