Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model
Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model
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DOI：
10.1007/s00526-013-0615-7
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发表时间：
2012-09
影响因子：
2.1
通讯作者：
Xiaosen Han;G. Tarantello
中科院分区：
文献类型：
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作者：
Xiaosen Han;G. Tarantello
本文建立了非线性椭圆型方程组双周期解存在性的一个多重性结果，该结果是在研究自对偶非Abel Chern-Simons涡时得到的。我们证明了当Chern-Simons耦合参数足够小时，系统至少有两个解;当耦合参数足够大时，系统不存在解.如Nolasco和Tarantello（Commun Math Phys 213：599-639，2000）中所述，我们使用问题的变分公式。因此，我们通过一个约束最小化方法得到第一个解决方案，并表明它是渐近规范等价的（破）主嵌入真空系统，作为。然后，我们得到了第二个解决方案的“山口”型的最小-最大程序。
In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions in anonlinear elliptic system arising in the study of self-dual non-Abelian Chern–Simons vortices. We show that the system admits at least two solutions when the Chern–Simons coupling parameteris sufficiently small; while no solution exists forsufficiently large. As in Nolasco and Tarantello (Commun Math Phys 213:599–639, 2000), we use a variational formulation of the problem. Thus, we obtain a first solution via a constrained minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as. Then we obtain a second solution by a min-max procedure of “mountain pass” type.