REMARKS ON NONTOPOLOGICAL SOLUTIONS IN THE SELF-DUAL CHERN-SIMONS GAUGED O(3) SIGMA MODELS

Title & Authors
REMARKS ON NONTOPOLOGICAL SOLUTIONS IN THE SELF-DUAL CHERN-SIMONS GAUGED O(3) SIGMA MODELS
Choi, Nari; Han, Jongmin;

Abstract
In this paper, we prove the existence of nontopological solutions to the self-dual equations arising from the Chern-Simons gauged O(3) sigma models. The property of solutions depends on a parameter $\small{{\tau}{\in}[-1,1}$$\small{]}$$\small{}$ appearing in the nonlinear term. The case ${\tau} Keywords Chern-Simons gauged O(3) sigma model;nontopological solutions; Language English Cited by References 1. D. Chae and O. Y. Imanuvilov, The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000), no. 1, 119-142. 2. H. Chan, C.-C. Fu, and C.-S. Lin, Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation, Comm. Math. Phys. 231 (2002), no. 2, 189-221. 3. X. Chen, S. Hastings, J. B. McLeod, and Y. Yang, A nonlinear elliptic equation arising from gauge field theory and cosmology, Proc. Roy. Soc. London Ser. A 446 (1994), no. 1928, 453-478. 4. K. Choe, Existence of nontopological solutions in the Chern-Simons gauged O(3) sigma models, Preprint. 5. K. Choe and J. Han, Existence and properties of radial solutions in the self-dual ChernSimons O(3) sigma model, J. Math. Phys. 52 (2011), no. 8, 082301, 20 pp. 6. K. Choe, J. Han, and C.-S. Lin, Bubbling solutions for the Chern-Simons gauged O(3) sigma model in$\mathbb{R}^2$, Discrete Contin. Dyn. Syst. 34 (2014), no. 7, 2703-2728. 7. K. Choe, J. Han, C.-S. Lin, and T.-C. Lin, Uniqueness and solution structure of nonlinear equations arising from the Chern-Simons gauged O(3) sigma models, J. Differential Equations 255 (2013), no. 8, 2136-2166. 8. K. Choe, N. Kim, and C.-S. Lin, Existence of self-dual non-topological solutions in the Chern-Simons Higgs model, Ann. Inst. H. Poincare Anal. Non Lineaire 28 (2011), no. 6, 837-852. 9. K. Choe and H.-S. Nam, Existence and uniqueness of topological multivortex solutions of the self-dual Chern-Simons CP(1) model, Nonlinear Anal. 66 (2007), no. 12, 2794-2813. 10. J. Han and H. Huh, Existence of solutions to the self-dual equations in the Maxwell gauged O(3) sigma model, J. Math. Anal. Appl. 386 (2012), no. 1, 61-74. 11. J. Hong, Y. Kim, and P. Y. Pac, Multi-vortex solutions of the Abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990), no. 19, 2230-2233. 12. R. Jackiw and E. J. Weinberg, Self-dual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990), no. 19, 2234-2237. 13. K. Kimm, K. Lee, and T. Lee, Anyonic Bogomol'nyi solitons in a gauged O(3) sigma model, Phys. Rev. D 53 (1996), 4436-4440. 14. W.-M. Ni, On the elliptic equation${\Delta}u$+$K(x)u^{(n+1)/(n-2)}\$ = 0, its generalizations, and applications in geometry, Indiana Univ. Math. J. 31 (1982), no. 4, 493-529.

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