Abstract
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 inR 2 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.
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Communicated by A. Jaffe
Research supported in part by NSF grant DMS-88-02858 and DOE grant DE-FG02-86ER250125
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Spruck, J., Yang, Y. The existence of non-topological solitons in the self-dual Chern-Simons theory. Commun.Math. Phys. 149, 361–376 (1992). https://doi.org/10.1007/BF02097630
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DOI: https://doi.org/10.1007/BF02097630