Classification and nondegeneracy of SU(n+1) Toda system with singular sources

By Changshou Lin, Jun-cheng Wei, D. Ye. 2011

104 citations recorded by the source corpus.

AbstractWe consider the following Toda system where γi>−1, δ0 is Dirac measure at 0, and the coefficients aij form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: $$\sum_{j=1}^n a_{ij}\int_{\mathbb{R}^2}e^{u_j} dx = 4\pi(2+\gamma _i+\gamma_{n+1-i}), \quad\forall\;1\leq i \leq n.$$ This generalizes the classification result by Jost and Wang for γi=0, $\forall\;1\leq i\leq n$. (ii) We prove that if γi+γi+1+⋯+γj∉ℤ for all 1≤i≤j≤n, then any solution ui is radially symmetric w.r.t. 0. (iii) We prove that the linearized equation at any solution is non-degenerate. These are fundamental results in order to understand the bubbling behavior of the Toda system.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ccc12ce6bea7e922e0307a464e9a0b68137229ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, background): “The analysis of (1) is motivated by the study of vortex type configurations (see for example [4], [11], [26], [62] and [24], [33], [47], [54], [60], [61], [64]) in the Electroweak theory of Glashow-Salam-Weinberg [44], and in Self-Dual Chern-Simons theories [37], [41], [42].”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “MR 2969276 Zbl 1258.35089 [Lin et al. 2012b] C.-S. Lin, J. Wei, and C. Zhao, “Sharp estimates for fully bubbling solutions of a SU(3) Toda system”, Geom.”