On non-topological solutions of the A2 and B2 Chern-Simons system
Journal
Memoirs of the American Mathematical Society
Journal Volume
239
Journal Issue
1132
Pages
1-100
Date Issued
2016
Author(s)
Abstract
For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form: (Equation Presented) 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 this equation is the question of the existence of non-topological solutions. In this paper, we consider the A2 and B2 case. We prove the existence of non-topological solutions under the condition that either N2 ΣN1j=1 pj = N1 ΣN2j=1 qj or N2 ΣN1j=1 pj ≈ N1 ΣN2j=1 qj and N1, N2 > 1, |N1 - N2| ≈ 1. We solve this problem by a perturbation from the corresponding A2 and B2 Toda system with one singular source.
Type
journal article