ASYMPTOTIC LIMITS FOR THE SELF-DUAL CHERN-SIMONS CP(1) MODEL

Title & Authors
ASYMPTOTIC LIMITS FOR THE SELF-DUAL CHERN-SIMONS CP(1) MODEL
HAN, JONG-MIN; NAM, HEE-SEOK;

Abstract
In this paper we study the asymptotics for the energy density in the self-dual Chern-Simons CP(1) model. When the sequence of corresponding multivortex solutions converges to the topological limit, we show that the field configurations saturating the energy bound converges to the limit function. Also, we show that the energy density tends to be concentrated at the vortices and antivortices as the Chern-Simons coupling constant $\small{\kappa}$ goes to zero.
Keywords
Chern-Simons CP(1) model;asymptotic limits;
Language
English
Cited by
1.
Bubbling solutions for the Chern–Simons gauged $$O(3)$$ O ( 3 ) sigma model on a torus, Calculus of Variations and Partial Differential Equations, 2015, 54, 2, 1275
2.
Nontopological solutions in the self-dual Maxwell–Chern–Simons gauged O(3) sigma model, Nonlinear Analysis: Theory, Methods & Applications, 2015, 118, 22
3.
Existence and uniqueness of topological multivortex solutions of the self-dual Chern–Simons model, Nonlinear Analysis: Theory, Methods & Applications, 2007, 66, 12, 2794
References
1.
F. Bethuel, H. Brezis, and F. Helein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. Partial Differential Equations 1 (1993), 123-148

2.
E. B. Bogomol'nyi, The stability of classical solutions, Soviet J. Nuclear Phys. 24 (1976), 449-454

3.
D. Chae and H. S. Nam, Multiple existence of the multivortex solutions of the self-dual Chern-Simons CP(1) Model on a doubly periodic domain, Lett. Math. Phys. 49 (1999), 297-315

4.
J. Han, Asymptotic limit for condensate solutions in the abelian Chern-Simone Higgs model, Proc. Amer. Math. Soc. 131 (2003), 1839-1845

5.
J. Han, Asymptotic limit for condensate solutions in the abelian Chern-Simons Higgs model II, Proc. Amer. Math. Soc. 131 (2003), 3827-3832

6.
G.'t Hooft, A property of electric and magnetic flux in non-abelian gauge theories, Nuclear Phys. B. 153 (1979), 141-160

7.
A. Jaffe and C. Taubes, Vortices and monopoles, structure of static gauge theories, Birkhauser Boston, 1980

8.
K. Kimm, K. Lee, and T. Lee, The self-dual Chern-Simons CP(N) models, Phys. Lett. B. 380 (1996), 303-307

9.
H.S.Nam, Asymptotics for the condensate multivortex solutions in the self-dual Chern-Simons CP(1) Model, J.Math.Phys.42 (2001), 5698-5712.