The existence of non-topological solitons in the self-dual Chern-Simons theory

Joel Spruck, Yisong Yang

Research output: Contribution to journalArticlepeer-review


In the recently discovered (2+1)-dimensional relativistic Chern-Simons model, self-duality can be achieved when the Higgs potential density assumes a special form for which both the asymmetric and symmetric vacua are ground state solutions. This important feature may imply the coexistence of static topological and non-topological vortex-like solutions in R2 but the latter have been rather elusive to a rigorous construction. Our main purpose in this paper is to prove the existence of non-topological radially symmetric N-vortex solutions in the self-dual Chern-Simons model. By a shooting method, we obtain a continuous family of gauge-distinct N-vortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.

Original languageEnglish (US)
Pages (from-to)361-376
Number of pages16
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Oct 1992

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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