Proceedings of the Steklov Institute of Mathematics

, Volume 270, Issue 1, pp 230–239 | Cite as

Adiabatic limit in the Ginzburg-Landau and Seiberg-Witten equations

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Abstract

We study an adiabatic limit in (2 + 1)-dimensional hyperbolic Ginzburg-Landau equations and 4-dimensional symplectic Seiberg-Witten equations. In dimension 3 = 2+1 the limiting procedure establishes a correspondence between solutions of Ginzburg-Landau equations and adiabatic paths in the moduli space of static solutions, called vortices. The 4-dimensional adiabatic limit may be considered as a complexification of the (2+1)-dimensional procedure with time variable being “complexified.” The adiabatic limit in dimension 4 = 2+2 establishes a correspondence between solutions of Seiberg-Witten equations and pseudoholomorphic paths in the moduli space of vortices.

Keywords

Modulus Space STEKLOV Institute Landau Equation Dynamic Solution Adiabatic Limit 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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