Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Topological solutions for the self-dual Chern-Simons $ CP(1)$ model with large Chern-Simons coupling constant

Author: Zhi-You Chen
Journal: Proc. Amer. Math. Soc. 144 (2016), 191-203
MSC (2010): Primary 35J15; Secondary 35A02
Published electronically: June 9, 2015
MathSciNet review: 3415588
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider the self-dual Chern-Simons $ CP(1)$
model in the whole plane $ \mathbf {R}^2$. After reducing to a single equation, we prove the uniqueness of topological multivortex solutions for the model if the Chern-Simons coupling parameter is sufficiently large.

References [Enhancements On Off] (What's this?)

  • [1] Z.-Y. Chen and J.-L. Chern, Uniqueness of Topological Solutions and Sharp Region of Flux for Radial Solutions to the Self-Dual Maxwell-Chern-Simons $ O(3)$ Sigma Model,(2014) submitted
  • [2] Jann-Long Chern, Zhi-You Chen, and Yong-Li Tang, Uniqueness of finite total curvatures and the structure of radial solutions for nonlinear elliptic equations, Trans. Amer. Math. Soc. 363 (2011), no. 6, 3211-3231. MR 2775804 (2012c:35149),
  • [3] Hsungrow Chan, Chun-Chieh Fu, and Chang-Shou Lin, Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation, Comm. Math. Phys. 231 (2002), no. 2, 189-221. MR 1946331 (2003m:58026),
  • [4] Kwangseok Choe, Jongmin Han, Chang-Shou Lin, and Tai-Chia 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. MR 3082457,
  • [5] Kwangseok Choe and Hee-Seok Nam, Existence and uniqueness of topological multivortex solutions of the self-dual Chern-Simons $ \bf C\rm P(1)$ model, Nonlinear Anal. 66 (2007), no. 12, 2794-2813. MR 2311639 (2008f:81156),
  • [6] Dongho Chae and Hee-Seok Nam, Multiple existence of the multivortex solutions of the self-dual Chern-Simons $ \mathbf {C}{\rm P}(1)$ model on a doubly periodic domain, Lett. Math. Phys. 49 (1999), no. 4, 297-315. MR 1749573 (2001h:58023),
  • [7] Chiun Chuan Chen and Chang Shou Lin, Uniqueness of the ground state solutions of $ \Delta u+f(u)=0$ in $ {\bf R}^n,\;n\geq 3$, Comm. Partial Differential Equations 16 (1991), no. 8-9, 1549-1572. MR 1132797 (92j:35048),
  • [8] B. Gidas, Wei Ming Ni, and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $ {\bf R}^{n}$, Mathematical analysis and applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York-London, 1981, pp. 369-402. MR 634248 (84a:35083)
  • [9] Jongmin Han and Kyungwoo Song, Existence and asymptotics of topological solutions in the self-dual Maxwell-Chern-Simons $ {\rm O}(3)$ sigma model, J. Differential Equations 250 (2011), no. 1, 204-222. MR 2737840 (2012c:58052),
  • [10] Man Kam Kwong, Uniqueness of positive solutions of $ \Delta u-u+u^p=0$ in $ {\bf R}^n$, Arch. Rational Mech. Anal. 105 (1989), no. 3, 243-266. MR 969899 (90d:35015),
  • [11] Kyoungtae Kimm, Kimyeong Lee, and Taejin Lee, The self-dual Chern-Simons $ {\bf C}{\rm P}(N)$ models, Phys. Lett. B 380 (1996), no. 3-4, 303-307. MR 1398394 (97h:81116),
  • [12] Congming Li, Local asymptotic symmetry of singular solutions to nonlinear elliptic equations, Invent. Math. 123 (1996), no. 2, 221-231. MR 1374197 (96m:35085),

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35J15, 35A02

Retrieve articles in all journals with MSC (2010): 35J15, 35A02

Additional Information

Zhi-You Chen
Affiliation: Department of Mathematics, National Central University, Chung-Li 32001, Taiwan

Received by editor(s): June 6, 2014
Received by editor(s) in revised form: November 27, 2014
Published electronically: June 9, 2015
Additional Notes: The work of the author was partially supported by the Ministry of Science and Technology, Taiwan (No. MOST-103-2115-M-008-011-MY3) and the National Natural Foundation of China (No. 11401144)
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society