Local profile of fully bubbling solutions to SU(n+1) Toda systems

Abstract

We prove that for locally defined singular SU(n+1) Toda systems in ℝ2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of Lin-Wei-Ye [22] and the non-degeneracy of the linearized Toda system [22], which let us overcome the difficulties that come from lack of symmetry and the singular source.