On non-Topological solutions of the G2 Chern-Simons system
Journal
Communications in Analysis and Geometry
Journal Volume
24
Journal Issue
4
Pages
717-752
Date Issued
2016
Author(s)
Abstract
For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form where K is the Cartan matrix of rank 2. There are three Cartan matrix of rank 2: A2, B2 and G2. A long-standing open problem for (0.1) is the question of the existence of non-Topological solutions. In a previous paper [1], we have proved the existence of non-Topological solutions for the A2 and B2 Chern-Simons system. In this paper, we continue to consider the G2 case. We prove the existence of non-Topological solutions under the condition that either N2 N1 j=1 pj = N1 N2 j=1 qj or N2 Σ N1 j=1 pj = N1 Σ N2 j=1 qj and N1, N2 Σ > 1, N1 Σ - N2 = 1. We solve this problem by a perturbation from the corresponding G2 Toda system with one singular source. Combining with [1], we have proved the existence of nontopological solutions to the Chern-Simons system with Cartan matrix of rank 2.
Type
journal article