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

TL;DR

This paper characterizes the local behavior of fully bubbling solutions to singular SU(n+1) Toda systems in the plane, showing they can be approximated by global solutions despite challenges from singularities.

Contribution

It introduces a new approach combining classification and non-degeneracy results to analyze solutions near singular sources in Toda systems.

Findings

Profiles of bubbling solutions are accurately approximated by global solutions.

The approach overcomes symmetry and singularity challenges in the analysis.

Provides a framework for understanding singular Toda systems in two dimensions.

Abstract

In this article we prove that for locally defined singular SU(n+1) Toda systems in 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 and the non-degeneracy of the linearized Toda system, which make us overcome the difficulties that come from the lack of symmetry and the singular source.