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Multivortex solutions of the abelian Chern-Simons-Higgs theory. (English) Zbl 1014.58500
Summary: We have examined vortex solutions in \((2+1)\)D Chern-Simons-Higgs theory which has no usual Maxwell term. It is shown that the Bogomol’nyi-type equations can be derived for a simple sixth-order Higgs potential and corresponding general \(n\)-vortex solutions should contain \(2n\) free parameters. Various characteristics of Chern-Simons vortices are discussed briefly.

MSC:
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
35Q60 PDEs in connection with optics and electromagnetic theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
81T13 Yang-Mills and other gauge theories in quantum field theory
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