竞争Chern-Simons模型的一类新的非拓扑冒泡解
A new type of non-topological bubbling solutions to a competitive Chern-Simons model
摘要：
研究了$\mathbb{R}^2$中的非交换Chern-Simons系统，包括单李代数$A_2$和$B_2$ .在以前的工作中，我们证明了径向非拓扑解的存在性与规定的渐近行为通过度理论。我们还构造了一个序列的冒泡的解决方案，只有一个组件部分爆破在无穷远。本文利用打靶论证构造了另一类径向非拓扑起泡解序列。这些冒泡解的一个分量局部收敛于Chern-Simons-Higgs标量方程的非拓扑解，但这两个分量在无穷远处的不同区域同时部分爆破。这概括了Choe、Kim和第二作者最近的工作，其中研究了$SU(3)$病例（即$A_2$）。我们的结果甚至对于$SU(3)$情况也是新的，并且也证实了$SU(3)$情况和$B_2$情况之间的差异。
英文摘要：
We study a non-Abelian Chern-Simons system in $\mathbb{R}^2$, including the simple Lie algebras $A_2$ and $B_2$. In a previous work, we proved the existence of radial non-topological solutions with prescribed asymptotic behaviors via the degree theory. We also constructed a sequence of bubbling solutions with only one component blowing up partially at infinity. In this paper, we construct a sequence of radial non-topological bubbling solutions of another type via the shooting argument. One component of these bubbling solutions locally converge to a non-topological solution of the Chern-Simons-Higgs scalar equation, but both components blow up partially in different regions at infinity at the same time. This generalizes a recent work by Choe, Kim and the second author, where the $SU(3)$ case (i.e. $A_2$) was studied. Our result is new even for the $SU(3)$ case and also confirms the difference between the $SU(3)$ case and the $B_2$ case.
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