The existence of non-topological solitons in the self-dual Chern-Simons theory |
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Authors: | Joel Spruck Yisong Yang |
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Institution: | 1. Department of Mathematics, University of Massachusetts, 01003, Amherst, MA, USA 2. I.H.E.S., Bures-Sur-Yvette, France 3. Department of Mathematics and Statistics, University of New Mexico, 87131, Albuquerque, NM, USA
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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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