On the asymptotic behavior of solutions for the self-dual Maxwell-Chern-Simons \(O(3)\) sigma model. (English) Zbl 1498.35224
Summary: In this paper, we consider the nonlinear equations arising from the self-dual Maxwell-Chern-Simons gauged \(O(3)\) sigma model on \((2+1)\)-dimensional Minkowski space \(\mathbf{R^{2,1}}\) with the metric \(\mathrm{diag}(1,-1,-1)\). We establish the asymptotic behavior of multivortex solutions corresponding to their flux and find the range of the flux for non-topological solutions. Moreover, we prove the radial symmetry property under certain conditions in one vortex point case.
MSC:
| 35J47 | Second-order elliptic systems |
| 35J61 | Semilinear elliptic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
References:
| [1] | A.-A. Bogomol’nyi, The stability of classical solutions, Sov. J. Nucl. Phys., 24, 449-454 (1976) |
| [2] | D. Chae; O. Yu. Imanuvilov, Non-topological multivortex solutions to the self-dual Maxwell-Chern-Simons-Higgs systems, J. Funct. Anal., 196, 87-118 (2002) · Zbl 1079.58009 · doi:10.1006/jfan.2002.3988 |
| [3] | D. Chae and N. Kim, Vortex condensates in the relativistic self-dual Maxwell-Chern-Simons-Higgs system, RIM-GARC Preprint, (1997), 97-50. |
| [4] | W. Chen; C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63, 615-622 (1991) · Zbl 0768.35025 · doi:10.1215/S0012-7094-91-06325-8 |
| [5] | Z.-Y. Chen and J.-L. Chern, Sharp range of flux and the structure of solutions for the self-dual Maxwell-Chern-Simons \(O(3)\) Sigma model, submitted. |
| [6] | Z.-Y. Chen; J.-L. Chern, The analysis of solutions for Maxwell-Chern-Simons \(O(3)\) Sigma model, Calculus of Variations and Partial Differential Equations, 58, 147 (2019) · Zbl 1421.35085 · doi:10.1007/s00526-019-1590-4 |
| [7] | K.-S. Cheng; C.-S. Lin, On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in \({\bf{R}}^2\), Math. Annalen, 308, 119-139 (1997) · Zbl 0871.35014 · doi:10.1007/s002080050068 |
| [8] | J.-L. Chern; Z.-Y. Chen; H.-Y. Shen, Classification of solutions for self-dual Chern-Simons \(CP(1)\) Model, J. Math. Phys., 62, 031510 (2021) · Zbl 1461.81082 · doi:10.1063/5.0022001 |
| [9] | K. Choe and J. Han, Existence and properties of radial solutions in the self-dual Chern-Simons O(3) sigma model, J. Math. Phys., 52 (2011), 082301, 20 pp. · Zbl 1272.81112 |
| [10] | K. Choe; J. Han; C.-S. Lin; T.-C. Lin, Uniqueness and solution structure of nonlinear equations arising from the Chern-Simons gauged O(3) sigma models, J. Differential Equations, 255, 2136-2166 (2013) · Zbl 1287.81079 · doi:10.1016/j.jde.2013.06.010 |
| [11] | J. Han; H. Huh, Existence of solutions to the self-dual equations in the Maxwell gauged O(3) sigma model, J. Math. Anal. Appl., 386, 61-74 (2012) · Zbl 1229.35222 · doi:10.1016/j.jmaa.2011.07.046 |
| [12] | J. Han and J. Jang, Nontopological bare solutions in the relativistic self-dual Maxwell-Chern-Simons-Higgs model, J. Math. Phys., 46 (2005), 042310, 16 pp. · Zbl 1067.81094 |
| [13] | J. Han; H.-S. Nam, On the topological multivortex solutions of the self-dual Maxwell-Chern-Simons gauged O(3) sigma model, Lett. Math. Phys., 73, 17-31 (2005) · Zbl 1115.58018 · doi:10.1007/s11005-005-8443-0 |
| [14] | J. Han; K. Song, Existence and asymptotic of topological solutions in the self-dual Maxwell-Chern-Simons \(O(3)\) Sigma model, J. Diff. Eqn., 250, 204-222 (2011) · Zbl 1204.81116 · doi:10.1016/j.jde.2010.08.003 |
| [15] | K. Kim, K. Lee and T. Lee, Anyonic Bogomol’nyi solitons in a gauged \(O(3)\) sigma model, Phys. Rev. D, 53 (1996), 4436-4440. |
| [16] | T. Ricciardi, Asymptotics for Maxwell-Chern-Simons multivortices, Nonlinear. Anal. TMA, 50, 1093-1106 (2002) · Zbl 1079.58504 · doi:10.1016/S0362-546X(01)00752-0 |
| [17] | T. Ricciardi; G. Tarantello, Vortices in the Maxwell-Chern-Simons theory, Comm. Pure Appl. Math., 53, 811-851 (2000) · Zbl 1029.35207 · doi:10.1002/(SICI)1097-0312(200007)53:7<811::AID-CPA2>3.0.CO;2-F |
| [18] | B.-J. Schroers, Bogomol’nyi solitons in a gauged \(O(3)\) sigma model, Phys. Lett. B, 356, 291-296 (1995) · doi:10.1016/0370-2693(95)00833-7 |
| [19] | K. Song, Radial symmetry of topological solitons in the self-dual Maxwell-Chern-Simons \(O(3)\) Sigma model, Bull. Korean. Math. Soc., 48, 1111-1117 (2011) · Zbl 1225.81129 · doi:10.4134/BKMS.2011.48.5.1111 |
| [20] | Y. Yang, Solitons in Field Theory and Nonlinear Analysis, Springer Monographs in Mathematics, Springer-Verlag, New York, 2001. · Zbl 0982.35003 |
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