Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions

By Jürgen Jost, Changshou Lin, Guofang Wang. 2005

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In this paper, we continue to consider the 2-dimensional (open) Toda system (Toda lattice) for $SU(N+1)$. We give a much more precise bubbling behavior of solutions and study its existence in some critical cases

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a75fd374a8509e371e812184fce7f79988f14a83

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Citations in the corpus

Elliptic functions, Green functions and the mean field equations on tori (2006, background): “The mean field equation on a flat torus T takes the form ( 2 RC) (1.2) 4uC eu D ı0: This equation has its origin in the prescribed curvature problem in geometry like the Nirenberg problem, cone metrics etc.”
Classification of blowup limits for SU(3) singular Toda systems (2013, methodology): “For A = A2, [Jost et al. 2006] proved |uki (e −λk/2 y+ xk)− λk − vi (y)| ≤ C for x ∈ k, i = 1, 2.”
Moser-Trudinger and logarithmic HLS inequalities for systems (2005, methodology): “18) In fact, Jost and Wang studied in [11] a special system of this type, the Toda system, which corresponds to the case where A is the Cartan matrix for SU(n+ 1), i.”
Profile of bubbling solutions to a Liouville system (2009, background): “First we note that since every entire solution of the Liouville system satisfies (1.5), ∫ R2 hkn(0)e V kn is uniquely determined by (b) and∑ ij aij ∫ R2 hki (0)e V ki ∫ R2 hkj (0)e V kj = 8π ∑ i ∫ R2 hki (0)e V ki .”
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004, background): “…Chae and Imanuvilov (2000), Chang and Yang (1987), Chen and Lin (2001, 2002, 2003, to appear), Chipot et al. (1997), Ding et al. (1997, 1999), Jost and Wang (2001), Li (1999), Li and Shafrir (1994), Lin (2000), Nolasco and Tarantello (1998, 2000), Prajapat and Tarantello (2001), Struwe and…”
Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, unknown): “As in [6,26], we say that a point x ∈ Ω is a γ -regular point if for some γ > 0, there exists a function ψ ∈ Cc(Ω), 0 ψ 1, with ψ = 1 in a neighborhood of x such that ∫”
The blow up analysis of solutions of the elliptic sinh-Gordon equation (2007, methodology): “For the blow-up analysis of the Toda system see [16, 17 ].”