Communications in Mathematical Physics

, Volume 149, Issue 2, pp 361–376 | Cite as

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

  • Joel Spruck
  • Yisong Yang


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 inR2 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 symmetricN-vortex solutions in the self-dual Chern-Simons model. By a shooting method, we obtain a continuous family of gauge-distinctN-vortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.


Neural Network Statistical Physic Soliton Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Joel Spruck
    • 1
    • 2
  • Yisong Yang
    • 3
  1. 1.Department of MathematicsUniversity of MassachusettsAmherstUSA
  2. 2.I.H.E.S.Bures-Sur-YvetteFrance
  3. 3.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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