Existence of self-dual non-topological solutions in the Chern–Simons Higgs model

Choe, Kwangseok ; Kim, Namkwon ; Lin, Chang-Shou

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 837-852 / Harvested from Numdam

Résumé

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

Abstract

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

Détail

Publié le : 2011-01-01

MR 2859930 | Zbl 1232.81031 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2011.06.003

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