Abstract
We prove existence results for the self-dual non-topological solutions in a Maxwell–Chern–Simons model with non-minimal coupling by using the perturbation argument. We also study the structure of radially symmetric non-topological solutions.
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Cantor M.: Elliptic operators and the decomposition of tensor fields. Bull. Am. Math. Soc. (N.S.) 5(3), 235–262 (1981)
Chae D., Imanuvilov O.Y.: The existence of non-topological multivortex solutions in the relativistic self-dual Chern–Simons theory. Commun. Math. Phys. 215(1), 119–142 (2000)
Chae D., Imanuvilov O.Y.: Non-topological multivortex solutions to the self-dual Maxwell–Chern–Simons–Higgs systems. J. Funct. Anal. 196, 87–118 (2002)
Chan H., Fu C.C., Lin C.S.: Non-topological multivortex solutions to the self-dual Chern–Simons–Higgs equation. Commun. Math. Phys. 231, 189–221 (2002)
Chen X., Hastings S., McLeod J., Yang Y.: A nonlinear elliptic equation arising from gauge field theory and cosmology. Proc. R. Soc. Lond. A 446, 453–478 (1994)
Christiansen H.R., Cunha M.S., Helayël-Neto J.A., Manssur L.R.U., Nogueira A.L.M.A.: N = 2-Maxwell–Chern–Simons model with anomalous magnetic moment coupling via dimensional reduction. Int. J. Mod. Phys. A 14(1), 147–159 (1999)
Christiansen H.R., Cunha M.S., Helayël-Neto J.A., Manssur L.R.U., Nogueira A.L.M.A.: Self-dual vortices in a Maxwell–Chern–Simons model with nonminimal coupling. Int. J. Mod. Phys. A 14(11), 1721–1735 (1999)
Dunne G.: Self-duality and Chern–Simons theories. Lecture Notes in Physics. Springer, Heidelberg (1995)
Han J., Huh H.: Self-dual vortices in a Maxwell–Chern–Simons model with non-minimal coupling. Lett. Math. Phys. 82(1), 9–24 (2007)
Hong J., Kim Y., Pac P.: Multivortex solutions of the abelian Chern–Simons–Higgs theory. Phys. Rev. Lett. 64(19), 2230–2233 (1990)
Jackiw R., Weinberg E.: Self-dual Chern–Simons vortices. Phys. Rev. Lett. 64(19), 2234–2237 (1990)
Lee T., Min H.: Bogomol’nyi equations for solitons in Maxwell–Chern–Simons gauge theories with the magnetic moment interaction term. Phys. Rev. D 50(12), 7738–7741 (1994)
Lee C., Lee K., Min H.: Self-dual Maxwell–Chern–Simons solitons. Phys. Lett. B 252(1), 79–83 (1990)
Lee B.H., Lee C., Min H.: Supersymmetric Chern–Simons vortex systems and fermion zero modes. Phys. Rev. D 45(12), 4588–4599 (1992)
McOwen R.C.: Conformal metrics in \({\mathbb{R}^2}\) with prescribed Gaussian curvature and positive total curvature. Indiana Univ. Math. J. 34(1), 97–104 (1985)
Navrátil P.: N = 2 supersymmetry in a Chern–Simons system with the magnetic moment interaction. Phys. Lett. B 365, 119–124 (1996)
Nielsen H.B., Olesen P.: Vortex-line models for dual-strings. Nucl. Phys. B 61, 45–61 (1973)
Paul S., Khare A.: Charged vortices in an abelian Higgs model with Chern–Simons term. Phys. Lett. B 174, 420–422 (1986)
Spruck J., Yang Y.: The existence of non-topological solitons in the self-dual Chern–Simons theory. Commun. Math. Phys. 149(2), 361–376 (1992)
Tarantello, G.: Selfdual gauge field vortices: an analytical approach. In: Progress in Nonlinear Differential Equations and Their Applications. Birkhäuser, Boston (2008)
Torres M.: Bogomol’nyi limit for nontopological solitons in a Chern–Simons model with anomalous magnetic moment. Phys. Rev. D 46(6), 2295–2298 (1992)
Yang Y.: Solitons in field theory and nonlinear analysis. Springer Monographs in Mathematics. Springer, Heidelberg (2001)
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Choe, K. Self-dual Non-topological Vortices in a Maxwell–Chern–Simons Model with Non-minimal Coupling. Lett Math Phys 87, 47–65 (2009). https://doi.org/10.1007/s11005-009-0294-7
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DOI: https://doi.org/10.1007/s11005-009-0294-7