A new type of non-topological bubbling solutions to a competitive Chern-Simons model

Abstract

We study a non-Abelian Chern-Simons system in R 2 , including the simple Lie algebras A 2 and B 2 . In a previous work, we proved the existence of radial non-topological solutions with prescribed asymptotic behaviors via the degree theory. We also constructed a sequence of bubbling solutions with only one component blowing up partially at infinity. In this paper, we construct a sequence of radial non-topological bubbling solutions of another type via the shooting argument. One component of these bubbling solutions locally converge to a non-topological solution of the Chern-Simons-Higgs scalar equation, but both components blow up partially in different regions at infinity at the same time. This generalizes a recent work by Choe, Kim and the second author, where the SU(3) case (i.e. A 2 ) was studied. Our result is new even for the SU(3) case and also confirms the difference between the SU(3) case and the B 2 case.

The asymptotic behavior of Chern–Simons Vortices for Gudnason Model

“…In order to obtain the existence result, they applied a minimization approach. For the recent developments of (1.1), we refer the readers to [15,19,20,23,30,35,37,38,44,53,61,73].…”

Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

“…Back to problem (1.1), a sequence of solutions are constructed with the behaviors as 2πβ ln |x| + O(1) at infinity with a free parameter β ∈ (2, 2(N − M )). Normally, this type of solutions are called as non-topological solutions, for instance [2,6,8,17] on non-topological solutions of Chern-Simon equation or systems. In particular, for β ∈ (2, 4), the author in [24, Chapter 2] gave an existence result of (1.3) and asserted that the solution converges to a constant at infinity.…”