New blow-up phenomena for SU(n+1) Toda system

2014/02/16 by Monica Musso, Angela Pistoia, Musso, Monica +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.3784

arXiv admin note: text overlap with arXiv:1210.5719

openalex publication_date 2014/02/16 · arxiv created 2016/04/13 · arxiv updated 2016/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the SU(n+1) Toda system (S_λ) \ \beginaligned Δu₁ + 2λe^u₁ - λe^u₂- … - λe^u_k = 0 \hboxin Ω,
Δu₂ - λe^u₁ + 2λe^u₂ - … - λe^u_k=0 \hboxin Ω,
⋮ \hskip3truecm \ddots \hskip2truecm ⋮
Δu_k -λe^u₁-λe^u₂- …+2λe^u_k=0 \hboxin Ω, u₁ = u₂ = … = u_k =0 \hboxon ∂Ω.
\endaligned. If 0∈Ω and Ω is symmetric with respect to the origin, we construct a family of solutions (u_1λ,…,u_kλ) to (S_λ) such that the i-th component u_iλ blows-up at the origin with a mass 2ⁱ⁺¹π as λ goes to zero.

Citations

• The blow up analysis of solutions of the elliptic sinh-Gordon equation
• A Topological Degree Counting for some Liouville Systems of Mean Field Equations
• Multiple Blow-Up Phenomena for the Sinh-Poisson Equation

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• A continuum of solutions for the SU(3) Toda System exhibiting partial blow-up

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