Local profile of fully bubbling solutions to $\mathrm{SU}(n+1)$ Toda systems

Abstract

In this article we prove that for locally defined singular $\mathrm{SU}(n+1)$ Toda systems in ${\mathbb{R}}^2$, 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.