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Classification of Solutions of a Toda System in R²
, 2001
"... In this paper, we consider solutions of the following (open) Toda system (Toda lattice) for SU(N + 1) \Gamma 1 2 \Deltau i = N X j=1 a ij e u j in R 2 ; for i = 1; 2; \Delta \Delta \Delta ; N , where K = (a ij ) N \ThetaN is the Cartan matrix for SU(N + 1). We show that any solution u = ( ..."
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Cited by 20 (3 self)
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In this paper, we consider solutions of the following (open) Toda system (Toda lattice) for SU(N + 1) \Gamma 1 2 \Deltau i = N X j=1 a ij e u j in R 2 ; for i = 1; 2; \Delta \Delta \Delta ; N , where K = (a ij ) N \ThetaN is the Cartan matrix for SU(N + 1). We show that any solution u = (u 1 ; u 2 ; \Delta \Delta \Delta ; uN ) with Z R 2 e u i ! 1; i = 1; 2; \Delta \Delta \Delta ; N; can be obtained from a rational curve in C P N .
CLASSIFICATION OF BLOWUP LIMITS FOR SU(3) SINGULAR TODA SYSTEMS
"... ABSTRACT. We prove that for singular SU(3) Toda systems, the weak limits of the energy belong to a finite set. For more general systems we prove a uniform estimate for fully blownup solutions. Our method uses a selection process and a careful study of the interaction of bubbling solutions. 1. ..."
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Cited by 10 (5 self)
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ABSTRACT. We prove that for singular SU(3) Toda systems, the weak limits of the energy belong to a finite set. For more general systems we prove a uniform estimate for fully blownup solutions. Our method uses a selection process and a careful study of the interaction of bubbling solutions. 1.
A note on compactness properties of the singular Toda system
"... In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through va ..."
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Cited by 2 (0 self)
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In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods.
Toda Equations, Ginvariant Connections and Plücker Formulae
"... this article we consider adapted maps / : S ! G=T of a Riemann surface S ..."
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this article we consider adapted maps / : S ! G=T of a Riemann surface S
Classification and nondegeneracy of SU(n + 1) . . .
 INVENT MATH
, 2012
"... We consider the following Toda system n∑ �ui + aij e uj = 4πγiδ0 in R 2 ∫, e ui dx < ∞, ∀ 1 ≤ i ≤ n, j=1 where γi> −1, δ0 is Dirac measure at 0, and the coefficients aij form the standard tridiagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quanti ..."
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We consider the following Toda system n∑ �ui + aij e uj = 4πγiδ0 in R 2 ∫, e ui dx < ∞, ∀ 1 ≤ i ≤ n, j=1 where γi> −1, δ0 is Dirac measure at 0, and the coefficients aij form the standard tridiagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result: n∑ aij j=1 R 2 e uj dx = 4π(2 + γi + γn+1−i), ∀ 1 ≤ i ≤ n. This generalizes the classification result by Jost and Wang for γi = 0, ∀ 1 ≤ i ≤ 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