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On Non-topological Solutions of the ${\bf A}_2$ and ${\bf B}_2$ Chern-Simons System


About this Title

Weiwei Ao, Chang-Shou Lin and Juncheng Wei

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 239, Number 1132
ISBNs: 978-1-4704-1543-3 (print); 978-1-4704-2747-4 (online)
DOI: http://dx.doi.org/10.1090/memo/1132
Published electronically: June 30, 2015

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Proof of Theorem 1.1 in the ${\bf A}_2$ case
  • Chapter 3. Proof of Theorem 1.1 in the ${\bf B}_2$ case
  • Chapter 4. Appendix

Abstract


For any rank 2 of simple Lie algebra, the relativistic Chern-Simons system has the following form:

* where is the Cartan matrix of rank . There are three Cartan matrix of rank 2: , and . A long-standing open problem for this equation is the question of the existence of non-topological solutions. In this paper, we consider the and case. We prove the existence of non-topological solutions under the condition that either or and . We solve this problem by a perturbation from the corresponding and Toda system with one singular source.

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