On non-topological solutions for planar Liouville Systems of Toda-type

TL;DR

This paper investigates the conditions for the existence of non-topological solutions in planar Liouville systems of Toda type, with implications for gauge field theories involving vortices.

Contribution

It provides necessary and sufficient conditions for radial solvability of these systems, extending known results to more general non-topological cases.

Findings

Identified conditions on flux pairs for solvability

Extended existence results to non-topological solutions

Developed a novel blow-up analysis method

Abstract

Motivated by the study of non abelian Chern Simons vortices of non topological type in Gauge Field Theory, we analyse the solvability of planar Liouville systems of Toda type in presence of singular sources. We identify necessary and sufficient conditions on the "flux" pair which ensure the radial solvability of the system. Since the given system includes the (integrable) 2 X 2 Toda system as a particular case, thus we recover the existence result available in this case. Our method relies on a blow-up analysis, which even in the radial setting, takes new turns compared with the single equation case.