On the Entire Radial Solutions of the Chern-Simons SU(3) System

TL;DR

This paper classifies all entire radial solutions of the self-dual SU(3) Chern-Simons equations, revealing their asymptotic behaviors and intersection properties, thus addressing a long-standing open problem in nonlinear systems.

Contribution

It provides a complete classification of entire radial solutions for the SU(3) Chern-Simons model, including their asymptotics and intersection properties.

Findings

All entire radial solutions are classified into topological, non-topological, and mixed types.

Asymptotic behaviors of solutions at infinity are fully characterized.

The components u and v intersect at most finitely many times.

Abstract

In this paper, we study the entire radial solutions of the self-dual equations arising from the relativistic SU(3) Chern-Simons model proposed by Kao-Lee and Dunne. Understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations. In this paper, we prove any entire radial solutions must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions. Even for radial solutions, this classification has remained an open problem for many years. As an application of this classification, we prove that the two components u and v have intersection at most finite times.