Comptes Rendus
Partial Differential Equations
On nondegeneracy of solutions to SU(3) Toda system
[Sur la nondégénérescence de solutions de SU(3) système de Toda]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 185-190.

On montre que pour toute solution de SU(3) système de Toda suivant Δu+2euev=0, Δveu+2ev=0 dans R2, R2eu<, R2ev<, le noyau de l'opérateur linéarisé associé est exactement de dimension huit, i.e., ce qu'on appelle la nondégénérescence.

We prove that the solution to the following SU(3) Toda system

{Δu+2euev=0,Δveu+2ev=0in R2,R2eu<,R2ev<,
is nondegenerate, i.e., the kernel of the associated linearized operator is exactly eight-dimensional.

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2010.11.025

Juncheng Wei 1 ; Chunyi Zhao 2 ; Feng Zhou 2

1 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
2 Department of Mathematics, East China Normal University, Shanghai, 200241, PR China
@article{CRMATH_2011__349_3-4_185_0,
     author = {Juncheng Wei and Chunyi Zhao and Feng Zhou},
     title = {On nondegeneracy of solutions to $ \mathit{SU}(3)$ {Toda} system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {185--190},
     publisher = {Elsevier},
     volume = {349},
     number = {3-4},
     year = {2011},
     doi = {10.1016/j.crma.2010.11.025},
     language = {en},
}
TY  - JOUR
AU  - Juncheng Wei
AU  - Chunyi Zhao
AU  - Feng Zhou
TI  - On nondegeneracy of solutions to $ \mathit{SU}(3)$ Toda system
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 185
EP  - 190
VL  - 349
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2010.11.025
LA  - en
ID  - CRMATH_2011__349_3-4_185_0
ER  - 
%0 Journal Article
%A Juncheng Wei
%A Chunyi Zhao
%A Feng Zhou
%T On nondegeneracy of solutions to $ \mathit{SU}(3)$ Toda system
%J Comptes Rendus. Mathématique
%D 2011
%P 185-190
%V 349
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2010.11.025
%G en
%F CRMATH_2011__349_3-4_185_0
Juncheng Wei; Chunyi Zhao; Feng Zhou. On nondegeneracy of solutions to $ \mathit{SU}(3)$ Toda system. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 185-190. doi : 10.1016/j.crma.2010.11.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.025/

[1] C.C. Chen; C.S. Lin Sharp estimates for solutions of multi-bubbles in compact Riemann surface, Comm. Pure Appl. Math., Volume 55 (2002) no. 6, pp. 728-771

[2] G. Dunne Self-dual Chern–Simons Theories, Lecture Notes in Physics, vol. 36, Springer, Berlin, 1995

[3] J. Jost; G.F. Wang Analytic aspects of the Toda system. I. A Moser–Trudinger inequality, Comm. Pure Appl. Math., Volume 54 (2001) no. 11, pp. 1289-1319

[4] J. Jost; G.F. Wang Classification of solutions of a Toda system in R2, Int. Math. Res. Not., Volume 2002 (2002) no. 6, pp. 277-290

[5] J. Jost; C.S. Lin; G.F. Wang Analytic aspects of Toda system. II. Bubbling behavior and existence of solutions, Comm. Pure Appl. Math., Volume 59 (2006) no. 4, pp. 526-558

[6] A.N. Leznov; M.V. Saveliev Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems, Progress in Physics, vol. 15, Birkhäuser, 1992

[7] J.Y. Li; Y.X. Li Solutions for Toda systems on Riemann surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci., Volume 5 (2005) no. 4, pp. 703-728

[8] A. Malchiodi; C.B. Ndiaye Some existence results for the Toda system on closed surfaces, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Math. Appl., Volume 18 (2007) no. 4, pp. 391-412

[9] H. Ohtsuka; T. Suzuki Blow-up analysis for SU(3) Toda system, J. Differential Equations, Volume 232 (2007) no. 2, pp. 419-440

[10] Y. Yang Solitons in Field Theory and Nonlinear Analysis, Springer Monographs in Mathematics, Springer, New York, 2001

Cité par Sources :

Commentaires - Politique