Multivortex solutions of the Abelian Chern-Simons-Higgs theory
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Publication:4491802
DOI10.1103/PhysRevLett.64.2230zbMath1014.58500OpenAlexW1992445470WikidataQ74501082 ScholiaQ74501082MaRDI QIDQ4491802
Yoonbai Kim, Jooyoo Hong, Pong Youl Pac
Publication date: 16 July 2000
Published in: Physical Review Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1103/physrevlett.64.2230
PDEs in connection with optics and electromagnetic theory (35Q60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)
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Cites Work
