Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6^th order potentials

Weiyue Ding, Jürgen Jost, Jiayu Li, Xiaowei Peng, and Guofang Wang

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Submission date: 19. Oct. 1998
Pages: 28
published in: Communications in mathematical physics, 217 (2001) 2, p. 383-407 
DOI number (of the published article): 10.1007/s002200100377
Bibtex
Keywords and phrases: chern-simons-higgs model, ginzburg-landau functional, seiberg-witten functional, self duality equations, exponential nonlinearity
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Abstract:
The abelian Chern-Simons-Higgs model of Hong-Kim-Pac and Jackiw-Weinberg leads to a Ginzburg-Landau type functional with a 6^th 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 6^th order potential and again show the existence of two asymptotically different solutions on a compact Kähler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations.