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: where δₚ denotes the Dirac measure at p∈Ω . When ⱼ¹\₁N₁= ⱼ²\₁N₂ , if we look for a solution with u₁=u₂=u , then (0.1) is reduced to the Chern‐Simons‐Higgs equation: 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 u₁≠ u₂ even if ⱼ¹\₁N₁=ⱼ²\₁N₂ .