Asymmetric blow-up for the SU(3) Toda System

TL;DR

This paper investigates asymmetric blow-up solutions in the SU(3) Toda system, demonstrating the existence of solutions where both components blow up at the same point with one component having a global mass, using singular perturbation techniques.

Contribution

It establishes the existence of a continuum of asymmetric blow-up solutions in the SU(3) Toda system with detailed blow-up behavior analysis.

Findings

Existence of solutions with simultaneous blow-up of both components.

Asymmetry in blow-up behavior with one component having global mass.

Application of singular perturbation methods to prove results.

Abstract

We consider the so-called Toda system in a smooth planar domain under homogeneous Dirichlet boundary conditions. We prove the existence of a continuum of solutions for which both components blow-up at the same point. This blow-up behavior is asymmetric, and moreover one component includes also a certain global mass. The proof uses singular perturbation methods.