Existence of self-dual non-topological solutions in the Chern–Simons Higgs model
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 6, p. 837-852

In this paper we investigate the existence of non-topological solutions of the Chern–Simons Higgs model in 2 . A long standing problem for this equation is: Given N vortex points and β>8π(N+1), does there exist a non-topological solution in 2 such that the total magnetic flux is equal to β/2? In this paper, we prove the existence of such a solution if β{8πNk k-1|k=2,,N}. We apply the bubbling analysis and the Leray–Schauder degree theory to solve this problem.

Lʼobjectif de cet article est de prouver lʼexistence de solutions non-topologiques du modèle de Chern–Simons Higgs dans 2 . Un problème de longue date existe pour cette équation : Soit N points vortex et β>8π(N+1), existe-t-il une solution non-topologique dans 2 telle que le flux magnétique total est égal à β/2 ? Dans cet article, nous prouvons lʼexistence dʼune solution pour β{8πNk k-1|k=2,,N}. Nous appliquons lʼanalyse par bulles et la theorie de Leray–Schauder pour résoudre ce problème.

DOI : https://doi.org/10.1016/j.anihpc.2011.06.003
Keywords: Semi-linear PDE, Non-topological vortices, Chern–Simons Higgs model
@article{AIHPC_2011__28_6_837_0,
     author = {Choe, Kwangseok and Kim, Namkwon and Lin, Chang-Shou},
     title = {Existence of self-dual non-topological solutions in the Chern--Simons Higgs model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {6},
     year = {2011},
     pages = {837-852},
     doi = {10.1016/j.anihpc.2011.06.003},
     zbl = {1232.81031},
     mrnumber = {2859930},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_6_837_0}
}
Choe, Kwangseok; Kim, Namkwon; Lin, Chang-Shou. Existence of self-dual non-topological solutions in the Chern–Simons Higgs model. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 6, pp. 837-852. doi : 10.1016/j.anihpc.2011.06.003. http://www.numdam.org/item/AIHPC_2011__28_6_837_0/

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