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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
45/1998

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

Abstract

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 Kähler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations.

Received:
Oct 19, 1998
Published:
Oct 19, 1998
Keywords:
chern-simons-higgs model, ginzburg-landau functional, seiberg-witten functional, self duality equations, exponential nonlinearity

Related publications

inJournal
2001 Repository Open Access
Weiyue Ding, Jürgen Jost, Jiayu Li, Xiaowei Peng and Guofang Wang

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

In: Communications in mathematical physics, 217 (2001) 2, pp. 383-407