an:01631838
Zbl 0994.58009
Ding, Weiyue; Jost, J??rgen; Li, Jiayu; Peng, Xiaowei; Wang, Guofang
Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6th order potentials
EN
Commun. Math. Phys. 217, No. 2, 383-407 (2001).
00074012
2001
j
58E30 35J60 53C99
Chern-Simons-Higgs model; Ginzburg-Landau type functional; 6th order potential; compact Riemann surface; Seiberg-Witten type functional; compact K??hler surface
Summary: The abelian Chern-Simons-Higgs model of Hong-Kim-Pac and Jackiw-Weinberg leads to a Ginzburg-Landau type functional with a 6th order potential on a compact Riemann surface. We derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0, for any number of prescribed vortices. We also introduce a Seiberg-Witten type functional with a 6th order potential and again show the existence of two asymptotically different solutions on a compact K??hler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations.